A car travelling at u mph has to make an emergency stop. There is an initial reaction time T₁ before the driver applies a constant braking deceleration of a mph². After a further time T₂ the car comes to rest. Show that T₂ = u/a and that the average speed during the braking period is u/2. Hence show that the total stopping distance D may be expressed in the form D = Au + Bu² where A and B depend on T₁ and a.

The stopping distances for a car travelling at 20 mph and 40 mph are 40 feet and 120 feet respectively. Estimate the stopping distance for a car travelling at 70 mph. A driver sees a hazard 150 feet ahead. What is the maximum possible speed of the car at that moment if a collision is to be avoided?