Motion Revision Notes

Speed is a measure of how quickly an object moves from one place to another. It tells us the rate at which distance changes with time. For example, if a car travels 100 metres in 5 seconds, its speed indicates how fast it covers that distance.

Speed is a scalar quantity, meaning it has magnitude only and no direction. This distinguishes it from velocity, which includes direction. In this objective, we focus on speed as the distance covered divided by the time taken.

• Speed measures how fast an object moves.
• It is a scalar quantity (magnitude only).
• Speed relates distance covered to the time taken.

The fundamental formula to calculate speed is: s = d / t, where:

s is speed, usually measured in metres per second (m/s).

d is distance covered, measured in metres (m).  - t is the time taken, measured in seconds (s).

• Speed (s) = Distance (d) ÷ Time (t)
• Units must be consistent: metres for distance, seconds for time.
• Speed is expressed in metres per second (m/s) in SI units.

Consider a cyclist who travels 300 metres in 60 seconds. To find the speed:

1. Identify the distance, d = 300 m, and time, t = 60 s.

2. Substitute into the formula: s = d / t = 300 m ÷ 60 s = 5 m/s.  3. The cyclist's speed is 5 metres per second, meaning they cover 5 metres every second on average.

• Identify distance and time from the problem.
• Substitute values into s = d/t.
• Calculate and include units in the answer.

Speed can vary depending on the situation. For example, a sprinter running 100 metres in 10 seconds has a speed of 10 m/s, while a walking person covering 100 metres in 100 seconds has a speed of 1 m/s. This shows how speed reflects the rate of motion.

In everyday life, speed is often measured in kilometres per hour (km/h). To convert from m/s to km/h, multiply by 3.6. For example, 5 m/s × 3.6 = 18 km/h. However, in scientific calculations, m/s is preferred for consistency.

• Speed varies with how fast an object moves.
• Common units include m/s and km/h.
• Conversion: 1 m/s = 3.6 km/h.

To measure speed practically, you need to measure the distance an object travels and the time it takes accurately. For example, using a stopwatch to time a runner over a measured track length.

Accuracy depends on precise measurement of distance and time. Repeating measurements and calculating an average speed improves reliability.

Safety is important when timing moving objects; ensure the area is clear and the method does not interfere with the motion.

• Measure distance and time accurately.
• Repeat measurements for reliability.
• Ensure safety during practical measurements.

Average speed is a way to describe how fast an object moves over a whole journey, regardless of any changes in speed during that time. It is calculated by dividing the total distance travelled by the total time taken. This gives a single value representing the overall speed for the entire trip.

Unlike instantaneous speed, which is the speed at a particular moment, average speed smooths out any variations, such as speeding up or slowing down. This makes it useful for summarising journeys where speed is not constant.

• Average speed = total distance ÷ total time
• It represents the overall speed for the entire journey
• It is different from instantaneous speed

The formula for average speed is: s = d ÷ t, where s is average speed, d is total distance, and t is total time. It is important to use consistent units for distance and time to get a correct speed value.

Common units for distance include metres (m) and kilometres (km), while time is often measured in seconds (s) or hours (h). The resulting speed units will be metres per second (m/s) or kilometres per hour (km/h).

For example, if distance is in kilometres and time in hours, the speed will be in km/h. If distance is in metres and time in seconds, the speed will be in m/s. Always convert units if necessary before calculating.

• Formula: average speed (s) = total distance (d) ÷ total time (t)
• Use consistent units: metres and seconds or kilometres and hours
• Speed units: m/s or km/h depending on units used

Suppose a cyclist travels 30 kilometres in 2 hours. To find the average speed, use the formula: s = d ÷ t.

Substitute the values: s = 30 km ÷ 2 h = 15 km/h. This means the cyclist’s average speed is 15 kilometres per hour.

If the same cyclist covered 15000 metres in 1800 seconds, first check units. Distance is in metres and time in seconds, so speed will be in m/s. Calculate: s = 15000 m ÷ 1800 s ≈ 8.33 m/s.

• Example 1: 30 km in 2 h → average speed = 15 km/h
• Example 2: 15000 m in 1800 s → average speed ≈ 8.33 m/s

When measuring average speed in experiments or real life, ensure accurate measurements of distance and time. Use appropriate instruments such as measuring tapes, odometers, stopwatches, or timers.

Repeat measurements to reduce random errors and calculate an average time or distance if possible.

Be aware that average speed does not show variations in speed during the journey. For example, if a car stops at traffic lights, the average speed includes the waiting time, which lowers the average compared to the car’s speed while moving.

• Use accurate instruments for distance and time
• Repeat measurements to improve reliability
• Average speed does not reflect speed changes during the journey

Sometimes you need to convert units before calculating average speed. For example, to convert kilometres to metres, multiply by 1000. To convert hours to seconds, multiply by 3600.

Example: A runner covers 5 km in 20 minutes. Convert 5 km to metres: 5 × 1000 = 5000 m. Convert 20 minutes to seconds: 20 × 60 = 1200 s. Then calculate average speed in m/s: 5000 m ÷ 1200 s ≈ 4.17 m/s.

Always check units before calculating to avoid errors and ensure your answer is in the desired unit.

• Convert km to m by multiplying by 1000
• Convert hours to seconds by multiplying by 3600
• Check units before calculating average speed

Distance-time graphs plot distance travelled (y-axis) against time elapsed (x-axis). They visually represent how far an object moves over time.

The slope (gradient) of a distance-time graph indicates the object's speed. A steeper slope means a higher speed because the object covers more distance in less time.

A horizontal line (zero slope) shows the object is stationary, as distance does not change with time. A straight line with constant slope indicates constant speed. A curved line shows changing speed (acceleration or deceleration).

• Distance on vertical axis, time on horizontal axis.
• Slope = change in distance ÷ change in time = speed.
• Horizontal line means stationary.
• Straight sloped line means constant speed.
• Curved line means changing speed.

Speed-time graphs plot speed (y-axis) against time (x-axis), showing how speed changes over time.

The slope of a speed-time graph represents acceleration. A positive slope means the object is speeding up; a negative slope means it is slowing down (decelerating).

The area under the speed-time graph corresponds to the distance travelled during that time interval. This is because speed × time = distance, and the graph area calculates this product visually.

• Speed on vertical axis, time on horizontal axis.
• Slope = change in speed ÷ change in time = acceleration.
• Positive slope = acceleration; negative slope = deceleration.
• Area under graph = distance travelled.

To create these graphs, first collect data of distance and time or speed and time from an experiment or problem.

Plot the data points accurately on graph paper or using software, labelling axes with correct units (metres, seconds, metres per second).

Draw a smooth curve or straight line through the points to represent the motion clearly. Avoid connecting points with jagged lines unless data is discrete events.

• Collect accurate data for distance/time or speed/time.
• Label axes with quantity and units.
• Plot points carefully and draw best-fit line or curve.
• Use consistent scales on axes for clarity.

From a distance-time graph, calculate speed by finding the slope between two points: speed = (change in distance) ÷ (change in time). For example, if distance changes from 10 m to 30 m over 4 seconds, speed = (30 - 10) m ÷ 4 s = 5 m/s.

From a speed-time graph, calculate acceleration by finding the slope: acceleration = (change in speed) ÷ (change in time). For example, speed increases from 2 m/s to 10 m/s in 4 seconds, acceleration = (10 - 2) m/s ÷ 4 s = 2 m/s².

Calculate distance travelled from a speed-time graph by finding the area under the curve. For constant speed, area is a rectangle (speed × time). For acceleration, area may be a trapezium or triangle, requiring appropriate area formulas.

• Speed = Δdistance ÷ Δtime from distance-time graph slope.
• Acceleration = Δspeed ÷ Δtime from speed-time graph slope.
• Distance = area under speed-time graph.
• Use geometric formulas for area: rectangle, triangle, trapezium.

Example 1: A cyclist travels 100 m in 20 s. Plot distance-time points (0,0), (20,100). The slope is 100 m ÷ 20 s = 5 m/s, constant speed.

Example 2: A car accelerates from 0 to 20 m/s in 5 s. On speed-time graph, slope = (20 - 0) m/s ÷ 5 s = 4 m/s² acceleration.

When drawing graphs, use a ruler for straight lines and smooth curves for acceleration. Label axes clearly and include units to avoid confusion.

• Calculate slopes carefully with units.
• Use area under speed-time graph to find distance.
• Label graphs fully for clarity.
• Practice sketching typical graph shapes for different motions.

Acceleration occurs when an object increases its speed over a period of time. It is a vector quantity, meaning it has both magnitude and direction, but in this context, we focus on the change in speed along a straight line.

For example, when a car moves from rest and speeds up to 20 m/s in 5 seconds, it is accelerating.

Mathematically, acceleration (a) is calculated by the change in velocity (Δv) divided by the time interval (Δt): a = Δv / Δt. Here, velocity is speed with direction, but if the direction is constant, acceleration relates directly to speed change.

• Acceleration means speeding up.
• It is calculated as change in velocity divided by time.
• Example: A car increasing speed from 0 to 20 m/s in 5 s has acceleration a = (20 - 0) / 5 = 4 m/s².

Deceleration is the term used when an object slows down, meaning its speed decreases over time. It is a specific case of acceleration where the acceleration value is negative relative to the direction of motion.

For instance, a cyclist slowing from 15 m/s to 5 m/s in 2 seconds is decelerating.

Using the formula a = Δv / Δt, the change in velocity is negative, indicating a reduction in speed.

• Deceleration means slowing down.
• It is negative acceleration along the direction of motion.
• Example: A cyclist slowing from 15 m/s to 5 m/s in 2 s has a = (5 - 15) / 2 = -5 m/s².

Both acceleration and deceleration describe how velocity changes with time. Velocity includes both speed and direction, so any change in speed or direction is acceleration.

In straight-line motion, acceleration increases speed, while deceleration decreases speed.

It is important to note that deceleration is not a separate type of motion but simply acceleration with a negative value relative to the chosen direction.

• Acceleration and deceleration are changes in velocity over time.
• Deceleration is negative acceleration in the direction of motion.
• Velocity change can be positive (speeding up) or negative (slowing down).

A car moving from a traffic light and increasing speed is accelerating.

A bus applying brakes to stop at a bus stop is decelerating.

A sprinter increasing speed after the start gun is accelerating, while slowing down after finishing is decelerating.

• Acceleration: car speeding up from rest.
• Deceleration: bus slowing to stop.
• Both involve changes in speed over time.

Speed-time graphs show how speed changes over time. A positive slope indicates acceleration, a negative slope indicates deceleration, and a flat line indicates constant speed.

For example, a speed-time graph with a line rising from 0 to 10 m/s over 4 seconds shows acceleration of (10 - 0) / 4 = 2.5 m/s².

Conversely, a line falling from 10 m/s to 0 over 5 seconds shows deceleration of (0 - 10) / 5 = -2 m/s².

• Positive slope on speed-time graph = acceleration.
• Negative slope = deceleration.
• Flat line = constant speed.

A distance-time graph is a visual representation showing how the distance of an object from a fixed point changes over time. The horizontal axis (x-axis) represents time, usually in seconds (s), while the vertical axis (y-axis) represents distance, usually in metres (m). By analysing the shape and slope of the graph, we can understand the motion of the object.

For example, if a car travels along a straight road, plotting its distance from the start against time produces a distance-time graph that reveals whether it is moving, stationary, or changing speed.

• Horizontal axis: time (s)
• Vertical axis: distance (m)
• Graph shows how distance changes over time

An object is stationary when it does not change its position over time. On a distance-time graph, this is shown by a horizontal line because the distance remains constant as time passes.

For instance, if a cyclist stops at a traffic light, the distance from the start does not increase or decrease during the stop. The graph line is flat (horizontal) during this period, indicating zero movement.

This horizontal line means the speed is zero because there is no change in distance over time.

• Horizontal line = stationary object
• Distance does not change with time
• Speed = 0 m/s

When an object moves at a constant speed, it covers equal distances in equal time intervals. On a distance-time graph, this is represented by a straight line that slopes upwards (if moving away from the start) or downwards (if returning).

The slope of this line is constant, meaning the speed does not change. The steeper the slope, the faster the object is moving.

For example, a runner jogging steadily along a track will produce a straight, diagonal line on the graph. If the line is steep, the runner is fast; if it is gentle, the runner is slower.

• Straight diagonal line = constant speed
• Slope = speed
• Steeper slope means higher speed

The slope of a distance-time graph is calculated as the change in distance divided by the change in time (rise over run). This slope directly represents the speed of the object.

Mathematically: speed = change in distance / change in time = Δd / Δt

For example, if the graph line rises 20 metres over 4 seconds, speed = 20 m ÷ 4 s = 5 m/s. This means the object moves at 5 metres per second during that time interval.

• Slope = Δdistance / Δtime
• Slope equals speed
• Example: 20 m in 4 s → speed = 5 m/s

If the distance-time graph slopes downwards, it means the distance from the starting point is decreasing. This indicates the object is moving back towards the start.

For example, a person walking back to their starting position after reaching a certain point will produce a graph line that slopes downwards.

The speed is still the slope's absolute value, but the direction is reversed.

• Downward slope = returning to start
• Distance decreases over time
• Speed is magnitude of slope

A speed-time graph plots an object's speed on the vertical axis against time on the horizontal axis. This graph visually represents how an object's speed changes over time, allowing us to interpret different types of motion by examining the shape and slope of the graph. Understanding these graphs is essential for analysing motion in physics.

• Vertical axis: speed (m/s)
• Horizontal axis: time (s)
• Graph shape shows how speed changes over time

An object is stationary when it is not moving, meaning its speed is zero. On a speed-time graph, this is shown by a horizontal line along the time axis at speed = 0 m/s. The flat line indicates no change in speed, and since the speed is zero, the object remains at rest during that time interval.

• Flat line at speed = 0 m/s
• No movement over time
• Example: A car stopped at a traffic light

When an object moves at a constant speed, its speed does not change over time. On the graph, this appears as a horizontal straight line above zero speed. The height of the line corresponds to the constant speed value. Since the speed remains steady, the slope of the graph is zero, indicating no acceleration or deceleration.

• Horizontal line above zero speed
• Speed value is constant
• Example: A cyclist moving steadily at 5 m/s

Acceleration means the object's speed is increasing over time. On a speed-time graph, acceleration is shown by a line with a positive slope, rising upwards as time progresses. The steeper the slope, the greater the acceleration. The slope of the graph equals the acceleration and can be calculated by dividing the change in speed by the change in time (a = Δv/Δt).

For example, if speed increases from 0 m/s to 10 m/s in 5 seconds, acceleration is (10 - 0) m/s ÷ 5 s = 2 m/s².

• Line slopes upwards
• Positive gradient indicates acceleration
• Calculate acceleration as slope = Δspeed/Δtime
• Example: Speed increases from 0 to 10 m/s in 5 s → a = 2 m/s²

Deceleration occurs when an object slows down, meaning its speed decreases over time. On the speed-time graph, this is represented by a line with a negative slope, descending as time increases. The slope is negative, indicating a reduction in speed. The magnitude of the slope gives the rate of deceleration.

For example, if speed decreases from 20 m/s to 5 m/s over 3 seconds, deceleration is (5 - 20) m/s ÷ 3 s = -5 m/s² (negative sign shows slowing down).

• Line slopes downwards
• Negative gradient indicates deceleration
• Calculate deceleration as slope = Δspeed/Δtime (negative value)
• Example: Speed drops from 20 to 5 m/s in 3 s → a = -5 m/s²

A distance-time graph plots the distance an object has travelled on the vertical (y) axis against the time elapsed on the horizontal (x) axis. Each point on the graph shows the distance from the starting point at a specific time.

Speed is how fast an object moves, defined as the distance covered per unit time. On a distance-time graph, speed corresponds to how quickly the distance changes as time passes.

If the graph is a straight line, the speed is constant. The slope (or gradient) of this line represents the speed. A steeper slope means the distance increases more rapidly with time, indicating a higher speed. A flat horizontal line means no change in distance over time, so the object is stationary.

• Distance is on the vertical axis; time is on the horizontal axis.
• Speed is the rate of change of distance with time.
• Slope of the graph = change in distance ÷ change in time.
• Steeper slope = higher speed; flat slope = zero speed.

To calculate speed from a distance-time graph, select a straight section where the speed is constant. Identify two points on this section with coordinates (time₁, distance₁) and (time₂, distance₂).

Calculate the change in distance (Δdistance) as distance₂ − distance₁ and the change in time (Δtime) as time₂ − time₁.

The speed is then calculated using the formula: Speed = Δdistance / Δtime. This is the gradient of the straight line segment on the graph.

• Choose two points on a straight section of the graph.
• Calculate Δdistance = distance₂ − distance₁.
• Calculate Δtime = time₂ − time₁.
• Calculate speed = Δdistance ÷ Δtime.
• Include units: metres (m) for distance and seconds (s) for time, so speed is in metres per second (m/s).

Suppose a graph shows an object moving from 0 m at 0 s to 20 m at 4 s along a straight line segment.

Calculate the change in distance: 20 m − 0 m = 20 m.

Calculate the change in time: 4 s − 0 s = 4 s. Then speed = 20 m ÷ 4 s = 5 m/s. This means the object moves at a constant speed of 5 metres per second during this interval.

• Identify two points: (0 s, 0 m) and (4 s, 20 m).
• Δdistance = 20 m − 0 m = 20 m.
• Δtime = 4 s − 0 s = 4 s.
• Speed = 20 m ÷ 4 s = 5 m/s.

A straight, upward sloping line indicates constant speed. The steeper the line, the faster the speed.

A horizontal line means the object is stationary because distance does not change with time.

A curved line indicates changing speed (acceleration or deceleration), so the slope is not constant and speed cannot be calculated by a single gradient value.

• Straight line with positive slope = constant speed.
• Horizontal line = stationary object (speed = 0).
• Curved line = changing speed; slope varies along the curve.

Do not confuse the slope of a distance-time graph with speed if the graph is curved; only straight sections represent constant speed.

Always subtract coordinates in the correct order to find positive values for distance and time changes.

Include units in calculations and final answers to avoid losing marks in exams.

• Use only straight sections for speed calculation.
• Calculate Δdistance and Δtime carefully and consistently.
• Always write units for distance (m), time (s), and speed (m/s).

Acceleration describes how quickly an object's speed changes when it moves along a straight path. It is not just about moving faster; acceleration can also mean slowing down, which is often called deceleration.

For example, if a car increases its speed from 10 m/s to 20 m/s, it is accelerating. If it reduces speed from 20 m/s to 10 m/s, it is decelerating, which is negative acceleration.

• Acceleration is the change in speed per unit time.
• It applies only to motion in a straight line for this context.
• Positive acceleration means speeding up; negative acceleration means slowing down.

Acceleration (a) is calculated by dividing the change in speed (Δv) by the time taken for that change (Δt). This is expressed as:

a = Δv / Δt, where: Δv = final speed − initial speed, and Δt = time interval over which the change occurs.

The units of acceleration are metres per second squared (m/s²), because speed is in metres per second (m/s) and time is in seconds (s).

• a = Δv / Δt, where Δv is in m/s and Δt is in s.
• Acceleration units are m/s².
• Calculate Δv by subtracting initial speed from final speed.

A cyclist increases speed from 5 m/s to 15 m/s in 4 seconds. To find the acceleration:

Step 1: Calculate change in speed, Δv = 15 m/s − 5 m/s = 10 m/s.

Step 2: Identify time interval, Δt = 4 s (given). Step 3: Apply formula: a = Δv / Δt = 10 m/s ÷ 4 s = 2.5 m/s². Step 4: Interpret result: The cyclist accelerates at 2.5 m/s², meaning their speed increases by 2.5 m/s every second.

• Identify initial and final speeds.
• Calculate Δv = final speed − initial speed.
• Divide Δv by Δt to find acceleration.
• Include units in final answer.

Positive acceleration means the object is speeding up. Negative acceleration, or deceleration, means the object is slowing down.

For example, if a car slows from 20 m/s to 10 m/s in 5 seconds:

Δv = 10 m/s − 20 m/s = −10 m/s (negative change), so a = −10 m/s ÷ 5 s = −2 m/s², indicating deceleration.

• Positive a: speed increases.
• Negative a: speed decreases (deceleration).
• Calculate Δv carefully to determine sign of acceleration.

In experiments measuring acceleration, ensure accurate timing and speed measurements. Use devices like stopwatches and motion sensors for precision.

Repeat measurements to reduce random errors and calculate an average acceleration.

Remember acceleration calculated here assumes straight line motion and uniform acceleration during the time interval. Real motion may be more complex.

• Use precise timing and speed measurement tools.
• Repeat trials and average results.
• Assume constant acceleration between measurements for calculations.

Acceleration is defined as the rate of change of velocity with respect to time. When an object’s velocity changes by equal amounts in equal time intervals, it is said to have constant acceleration. This means the acceleration value does not vary during the motion.

For example, if a car increases its speed by 2 m/s every second, its acceleration is constant at 2 m/s². Conversely, if the speed changes by different amounts in different seconds, the acceleration is not constant.

• Constant acceleration means velocity changes uniformly over time.
• Acceleration is calculated as change in velocity divided by change in time (a = Δv/Δt).

Given a table of speed and time data, constant acceleration can be determined by checking if the change in speed (Δv) over equal time intervals (Δt) is the same throughout.

For example, consider the following data for an object moving in a straight line:

| Time (s) | Speed (m/s) | | 0 | 0 | | 1 | 3 | | 2 | 6 | | 3 | 9 | | 4 | 12 | Here, the speed increases by 3 m/s every second, so acceleration is constant at 3 m/s² (a = 3 m/s ÷ 1 s). If the increments were not equal, acceleration would not be constant.

• Calculate acceleration between each pair of data points.
• If all calculated accelerations are equal, acceleration is constant.
• If accelerations differ, acceleration is variable.

A speed-time graph plots speed on the vertical axis and time on the horizontal axis. The shape of the graph reveals the nature of acceleration:

A straight line with a constant positive slope indicates constant positive acceleration (speed increasing uniformly).

A straight line with zero slope (horizontal line) indicates constant speed (zero acceleration).   - A straight line with a constant negative slope indicates constant negative acceleration (deceleration).  - A curved line indicates changing acceleration (non-uniform). For example, a line rising steadily from 0 m/s at 0 s to 10 m/s at 5 s is a straight line with slope 2 m/s², showing constant acceleration.

• Slope of speed-time graph = acceleration.
• Straight line slope means constant acceleration.
• Curved line means acceleration is changing.

The acceleration is the gradient (slope) of the speed-time graph. To calculate:

1. Choose two points on the straight section of the graph.

2. Calculate the change in speed (Δv) and change in time (Δt). 3. Use the formula a = Δv/Δt with units m/s². For example, if speed changes from 4 m/s to 12 m/s over 4 seconds, acceleration a = (12 - 4) m/s ÷ 4 s = 8 m/s ÷ 4 s = 2 m/s², confirming constant acceleration if the graph is a straight line.

• Use two points on the graph to find Δv and Δt.
• Calculate acceleration as a = Δv/Δt.
• Confirm constant acceleration if slope is uniform.

Suppose a cyclist’s speed is recorded every second:

| Time (s) | Speed (m/s) | | 0 | 0 | | 1 | 2 | | 2 | 4 | | 3 | 6 | | 4 | 8 | The speed increases by 2 m/s every second, indicating constant acceleration of 2 m/s². The speed-time graph would be a straight line with slope 2. If at any point the speed increment changed, the acceleration would not be constant.

• Check equal speed increments over equal time intervals.
• Plot speed-time graph to visually confirm straight line.
• Calculate acceleration using a = Δv/Δt to verify.

Acceleration is defined as the rate at which an object's speed changes with time. It can be positive (speeding up) or negative (slowing down, also called deceleration).

A speed-time graph plots speed on the vertical (y) axis and time on the horizontal (x) axis. The shape of the graph provides information about the motion of the object.

When the graph shows a straight line, it indicates that the acceleration is constant during that time interval. The slope of this straight line represents the acceleration.

• Acceleration = change in speed ÷ time taken
• Speed-time graph: speed on y-axis, time on x-axis
• Straight line section means constant acceleration

The slope of a straight line on a graph is calculated as the vertical change divided by the horizontal change.

On a speed-time graph, the vertical change is the change in speed (Δv), and the horizontal change is the change in time (Δt).

Therefore, acceleration (a) = Δv / Δt = (final speed - initial speed) / time interval.

• Slope = rise ÷ run = change in speed ÷ change in time
• Identify two points on the straight line section
• Calculate Δv = v(final) - v(initial)
• Calculate Δt = t(final) - t(initial)
• Divide Δv by Δt to find acceleration

Suppose a speed-time graph shows a straight line from 0 m/s at 0 seconds to 20 m/s at 5 seconds.

To find the acceleration, first identify the initial speed u = 0 m/s and final speed v = 20 m/s.

The time interval t = 5 s - 0 s = 5 s. Calculate acceleration: a = (v - u) / t = (20 m/s - 0 m/s) / 5 s = 4 m/s².

• Initial speed u = 0 m/s
• Final speed v = 20 m/s
• Time interval t = 5 s
• Acceleration a = (20 - 0) / 5 = 4 m/s²

Acceleration is measured in metres per second squared (m/s²), which means the speed changes by a certain number of metres per second every second.

A positive acceleration means the object is speeding up, while a negative acceleration (deceleration) means it is slowing down.

If the slope of the speed-time graph is zero (horizontal line), the acceleration is zero and the object moves at constant speed.

• Units of acceleration: m/s²
• Positive slope = speeding up
• Negative slope = slowing down (deceleration)
• Zero slope = constant speed

Do not confuse speed with velocity; speed-time graphs only show speed magnitude, so direction is not considered here.

Ensure you select two points on the same straight section of the graph to calculate the slope accurately.

Remember to subtract initial speed from final speed in the correct order to get the right sign for acceleration.

• Use points on the same straight line section
• Calculate Δv = final speed - initial speed
• Check units and convert if necessary
• Distinguish between speed and velocity concepts

A speed-time graph plots speed on the vertical axis and time on the horizontal axis. The graph shows how an object's speed changes over time.

The key concept is that the area under the graph between two time points corresponds to the distance travelled during that time interval.

For example, if the speed is constant, the graph is a horizontal straight line, and the area under this line forms a rectangle. If the speed changes at a constant rate (constant acceleration), the graph forms a straight sloping line, creating a triangle or trapezium shape under the curve.

• Speed on vertical axis, time on horizontal axis.
• Area under graph = distance travelled.
• Shape under graph depends on motion type.

When an object moves at constant speed, the speed-time graph is a horizontal line. The area under the graph is a rectangle with height equal to the speed and width equal to the time interval.

The distance travelled (d) can be calculated by multiplying speed (v) by time (t):

d = v × t (where d is in metres, v in metres per second, and t in seconds).

• Graph shape: rectangle.
• Formula: distance = speed × time.
• Example: Speed = 5 m/s, time = 10 s, distance = 5 × 10 = 50 m.

If an object accelerates or decelerates at a constant rate, the speed-time graph is a straight line sloping upwards or downwards.

The area under the graph forms a triangle or trapezium, depending on the initial speed.

If the initial speed is zero, the area is a triangle: area = ½ × base × height = ½ × time × final speed. This gives the distance travelled during acceleration from rest. For example, if an object accelerates from 0 to 8 m/s in 4 seconds, distance = ½ × 4 × 8 = 16 m.

• Graph shape: triangle or trapezium.
• Triangle area formula: ½ × base × height.
• Example: accelerating from 0 to 8 m/s in 4 s, distance = 16 m.

When the object starts with a non-zero speed and accelerates or decelerates at a constant rate, the area under the graph is a trapezium.

The trapezium area formula is: area = ½ × (sum of parallel sides) × height.

In speed-time graphs, the parallel sides are the initial and final speeds, and the height is the time interval. Thus: distance = ½ × (v_initial + v_final) × time.

• Graph shape: trapezium.
• Formula: distance = ½ × (initial speed + final speed) × time.
• Example: speed changes from 4 m/s to 10 m/s over 3 s, distance = ½ × (4 + 10) × 3 = 21 m.

An object moves with constant acceleration. Its speed increases from 2 m/s to 8 m/s over 5 seconds. Calculate the distance travelled during this time.

Step 1: Identify initial speed (v_i) = 2 m/s, final speed (v_f) = 8 m/s, time (t) = 5 s.

Step 2: Use trapezium area formula: distance = ½ × (v_i + v_f) × t = ½ × (2 + 8) × 5 = ½ × 10 × 5 = 25 m.

• Initial speed = 2 m/s, final speed = 8 m/s, time = 5 s.
• Distance = ½ × (2 + 8) × 5 = 25 m.
• Check units: speed in m/s, time in s, distance in m.

Acceleration is the rate at which an object's velocity changes over time. When this change results in an increase in speed, acceleration is positive. Conversely, when an object slows down, the change in velocity is negative, which is called deceleration or negative acceleration.

Deceleration is not a separate phenomenon but a specific case of acceleration where the velocity decreases. This means the acceleration value is negative, indicating a reduction in speed. Recognising this helps in correctly analysing motion where objects slow down, such as a car braking or a ball rolling to a stop.

• Acceleration can be positive (speeding up) or negative (slowing down).
• Deceleration is negative acceleration, indicating a decrease in velocity.
• Both acceleration and deceleration use the same formula but differ in sign.

The standard formula for acceleration is: \[ a = \frac{v_f - v_i}{t} \] where \( a \) is acceleration (m/s²), \( v_f \) is final velocity (m/s), \( v_i \) is initial velocity (m/s), and \( t \) is the time interval (s) over which the change occurs.

When an object slows down, \( v_f < v_i \), so \( v_f - v_i \) is negative, resulting in a negative acceleration value, which is deceleration.

For example, if a car slows from 20 m/s to 5 m/s in 3 seconds, the deceleration is: \[ a = \frac{5 - 20}{3} = \frac{-15}{3} = -5 \text{ m/s}^2 \] This negative value confirms the car is decelerating.

• Use \( a = (v_f - v_i)/t \) for all acceleration calculations.
• Negative results indicate deceleration.
• Include units in all calculations for clarity.

A negative acceleration value means the object’s velocity is decreasing. This is crucial when analysing motion graphs or solving problems involving slowing objects.

For example, in a speed-time graph, a downward slope indicates negative acceleration or deceleration.

Understanding this sign convention prevents confusion between speeding up and slowing down, ensuring correct answers in calculations and graph interpretations.

• Negative acceleration means velocity is decreasing.
• Downward slopes on speed-time graphs represent deceleration.
• Sign conventions are essential for correct problem-solving.

Consider a cyclist who slows from 12 m/s to 4 m/s over 2 seconds when applying brakes. Using the formula: \[ a = \frac{4 - 12}{2} = \frac{-8}{2} = -4 \text{ m/s}^2 \] The cyclist’s deceleration is 4 m/s².

Another example is a ball rolling to a stop, where its velocity decreases steadily until zero, showing negative acceleration.

These examples illustrate how deceleration is calculated and interpreted in real-world contexts.

• Calculate deceleration by substituting values into the acceleration formula.
• Real-life slowing motions demonstrate negative acceleration.
• Always check units and signs in calculations.

Deceleration is simply acceleration with a negative value, indicating a decrease in velocity.

Using the acceleration formula with correct sign interpretation allows accurate calculation of deceleration.

Recognising deceleration is essential for understanding motion, interpreting graphs, and solving physics problems involving slowing objects effectively.

• Deceleration = negative acceleration.
• Apply \( a = (v_f - v_i)/t \) carefully with attention to sign.
• Essential concept for motion analysis and problem-solving.

Acceleration due to gravity, symbolised as g, is the rate at which an object's velocity changes when it is falling freely under the influence of Earth's gravitational pull alone, without any other forces like air resistance acting on it.

This acceleration causes objects to speed up as they fall towards the Earth, increasing their velocity by a certain amount every second.

• It is a vector quantity directed towards the centre of the Earth.
• It describes how quickly an object gains speed when dropped or thrown downwards.

Near the Earth's surface, the acceleration due to gravity has an approximate value of 9.8 metres per second squared (9.8 m/s²). This means that every second, the velocity of a freely falling object increases by about 9.8 m/s.

For most practical calculations in physics, this value is treated as constant because variations due to altitude or location are very small and negligible.

For example, if an object starts from rest and falls freely for 3 seconds, its velocity after 3 seconds is approximately 3 × 9.8 = 29.4 m/s downward.

• g ≈ 9.8 m/s² near Earth's surface.
• This value varies slightly with altitude and latitude but is generally constant for everyday problems.

When an object is in free fall, the only force acting on it is gravity, causing it to accelerate downwards at g.

This acceleration affects the object's velocity and displacement over time, which can be calculated using kinematic equations assuming constant acceleration.

For example, the velocity v after time t is given by v = g × t (if starting from rest). The distance s fallen is s = ½ g t².

• Free fall assumes no air resistance.
• Acceleration remains constant at 9.8 m/s² during free fall.

All objects near Earth's surface accelerate at the same rate regardless of their mass because gravitational force and inertial resistance scale proportionally.

This means a heavy object and a light object dropped simultaneously from the same height will fall with the same acceleration and reach the ground at the same time (ignoring air resistance).

This principle was famously demonstrated by Galileo and is fundamental to understanding gravity.

• Acceleration due to gravity is independent of mass.
• Gravitational force and inertia balance to produce uniform acceleration.

In real situations, air resistance can affect falling objects, causing deviations from the ideal acceleration of 9.8 m/s².

At higher altitudes or different locations on Earth, g varies slightly due to Earth's shape and rotation, but these differences are small.

For precise scientific work, these variations are accounted for, but for most school-level physics problems, g = 9.8 m/s² is used as a constant.

• Air resistance reduces acceleration below 9.8 m/s².
• g varies slightly with altitude and latitude but is approximated as constant for simplicity.