Motion and forces Revision Notes

Kinetic Energy and Work Done

A moving vehicle possesses kinetic energy. When the vehicle brakes, work is done by the braking force to reduce this kinetic energy to zero. This work done is equal to the initial kinetic energy of the vehicle. The formula for kinetic energy is E_k = 0.5 * m * v^2, where m is mass and v is velocity. The formula for work done is W = F * d, where F is braking force and d is braking distance.

Relationship between Braking Distance and Initial Velocity

Since the work done by the braking force is equal to the initial kinetic energy, we have F * d = 0.5 * m * v^2. For a given vehicle, the mass (m) is constant. The maximum braking force (F) is also generally considered constant under consistent road conditions. Therefore, 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 will be four times greater. This non-linear relationship is why small increases in speed lead to significantly longer braking distances.