Stopping Distance on a Dry Road and a Wet Road
A car of mass 1200 kg is travelling at 20 m/s on a dry road. The driver sees a child step into the road 55 m ahead. The driver's reaction time is 0.75 s. The brakes then apply a constant braking force of 6000 N. The car's kinetic energy is transferred to thermal energy in the brakes and road. On the same road when wet, the maximum braking force falls to 4000 N, but the driver's reaction time is unchanged. A passenger says that because the car has a large mass, it will stop in a shorter distance, and that a 0.5 s reaction time would make the wet road safe. The teacher asks the group to use energy reasoning rather than only a formula, and to decide whether the car stops before reaching the child in each case.
1. Calculate the thinking distance, braking distance and total stopping distance on the dry road. Decide whether the car stops before reaching the child.
Read the worked answer
Thinking distance = speed × reaction time = 20 × 0.75 = 15 m.
Kinetic energy = ½mv² = ½ × 1200 × 20² = 240 000 J.
The brakes do work equal to force × braking distance, so:
6000 × d = 240 000
d = 40 m.
Total stopping distance = 15 + 40 = 55 m.
The child is 55 m ahead, so the car would stop only just at the child's position. That is not a safe margin: any small increase in reaction time, any delay in braking, or any reduction in braking force would mean the car hits the child. The correct judgement is that the situation is dangerous and the driver cannot rely on stopping in time.
2. The passenger says that a heavier car will stop in a shorter distance. Use energy reasoning to evaluate this claim.
Read the worked answer
The claim is not generally correct. For a given braking force F, the braking distance is found from:
F × d = ½mv²
so d = mv² / (2F).
If the braking force stays the same, increasing the mass increases the kinetic energy that must be removed and therefore increases the braking distance, not shortens it. In real braking, the maximum friction force may itself increase with the weight of the car, so mass can partly cancel out; but there is no reason for a heavier car to stop in a shorter distance. The passenger has confused mass with grip. A heavier car can have more tyre grip, but it also has more kinetic energy, and the safe conclusion is that mass does not make the car stop more quickly.
3. Calculate the stopping distance on the wet road with the original 0.75 s reaction time. Then test the claim that a 0.5 s reaction time would make the wet road safe.
Read the worked answer
On the wet road, thinking distance is still 15 m at 0.75 s.
Braking distance = KE / F = 240 000 / 4000 = 60 m.
Total stopping distance = 15 + 60 = 75 m, which is greater than 55 m, so the car would hit the child.
With a 0.5 s reaction time:
Thinking distance = 20 × 0.5 = 10 m
Total stopping distance = 10 + 60 = 70 m.
This is still greater than 55 m, so the claim is false. In fact, even with zero reaction time the wet braking distance alone is 60 m, which is already more than 55 m. Reducing reaction time helps, but it cannot make this situation safe; the speed must be lower or the braking force must be greater.