The Van Driver's Braking Distance
A van of mass 2000 kg travels at 15 m/s on a dry road. The driver sees a child step out 30 m ahead and brakes. The reaction time is 0.8 s. The braking force is 8000 N. A passenger says the van will stop in time because the braking distance is short. Another passenger says the total stopping distance matters, not just braking distance. The road is later wet, and the braking force falls to 5000 N. The driver's reaction time is unchanged. The child is still 30 m ahead when the driver first sees them.
1. Calculate the thinking distance, braking distance and total stopping distance on the dry road, and judge whether the van stops in time.
Read the worked answer
Thinking distance = speed × reaction time = 15 × 0.8 = 12 m. Braking distance comes from work and energy: kinetic energy = ½mv² = ½ × 2000 × 15² = 225 000 J. Work done by the braking force = force × distance, so distance = 225 000 ÷ 8000 = 28.1 m. Total stopping distance = 12 + 28.1 = 40.1 m. This is greater than 30 m, so the van does not stop in time. The passenger who focused on braking distance alone was wrong: thinking distance adds 12 m before braking even begins. Even with perfect brakes the van needs about 40 m, so the judgement must use total stopping distance.
2. Repeat the judgement for the wet road and explain why the change in outcome occurs.
Read the worked answer
Thinking distance is unchanged at 12 m because speed and reaction time are the same. Kinetic energy is still 225 000 J. With 5000 N braking force, braking distance = 225 000 ÷ 5000 = 45 m. Total stopping distance = 12 + 45 = 57 m, far beyond 30 m. The wet road reduces friction between tyres and road, so the maximum braking force is smaller. The same kinetic energy must be removed by a smaller force, so the distance over which work is done must be larger. The outcome changes from a near miss (40 m) to a serious collision risk (57 m). This shows that stopping distance depends on road conditions as well as speed, and that reaction time contributes a fixed distance that no braking improvement can remove.