Braking a car

When a driver sees a potential hazard ahead, the first thing he will do is to brake the car. This locks the wheels of the car, causing the car to skid on the road. The friction between the tyres and the road decelerates the car. If the driver takes this action fast enough, the car will stop in a short period of time, hence avoiding collision with other vehicles or injuring pedestrians. Due to the delay in human reaction, however, there is always a time lag between seeing a hazard and braking the car. This time interval is known as reaction time, which is about 0.75 s and may vary widely for different persons. During the reaction time the car travels a distance known as reaction distance (Fig. 6-1):

After the reaction time, the brake is applied and the car decelerates. It takes another distance, which is known as the braking distance, for the car to stop completely. The total distance that the car has travelled after the driver seeing the hazard is known as the stopping distance. It is equal to

Fig. 6-1 The reaction distance and the braking distance.

Flash animation: Braking a car

We should make the stopping distance as small as possible to prevent accidents. Both the reaction distance and the braking distance depend on the initial speed of the car. The higher the speed of the car, the longer distance it has to travel before coming to rest. Speeding is often a major cause of traffic accidents because the driver cannot stop the car in time in an emergency. The braking distance also depends on the friction between the tyres and road. It would increase greatly if the road is wet, or tyres of poor quality are used.

We can estimate the braking distance of a car if its deceleration is known. In the following section we will derive several equations of motion relating the time, displacement, velocity and acceleration for a uniformly accelerated motion. The equations will then be applied to estimate the braking distances of a car travelling at different speeds.