Motion and forces Study Guide

When a vehicle is braking, its kinetic energy (the energy of motion) is converted into other forms, primarily heat and sound, due to friction between the tyres and the road, and within the braking system. The work done by the braking force to bring the vehicle to rest is equal to the initial kinetic energy of the vehicle. Kinetic energy is calculated using the formula E_k = 0.5 * m * v^2, where 'm' is the mass and 'v' is the initial velocity. Work done is calculated as W = F * d, where 'F' is the braking force and 'd' is the braking distance. Since W = E_k, it follows that F * d = 0.5 * m * v^2. If we assume the braking force (F) and the mass (m) of the vehicle remain constant, then the braking distance (d) is directly proportional to the square of the initial velocity (v^2). This means that if the initial velocity doubles, the braking distance increases by a factor of four (2^2). This relationship is crucial for understanding road safety and vehicle performance.