When a force is applied to the brakes of a vehicle, there is work done on the friction between the brakes and the wheel. This reduces the kinetic energy of the vehicle, slowing it down and causing the temperature of the brakes to increase.
Decelerating from very high speeds too quickly can cause a number of problems:
Car safety features such as seatbelts, airbags and crumple zones are all designed to deform (stretch or squash) slowly, which increases the time taken to stop the car. Since the change in speed happens in a longer time, there is less deceleration and, therefore less force required. This also decreases the force of the deceleration on any people within the car.
Newton's second law can be used to estimate the forces involved in braking.
70 miles per hour is the same as 31 metres per second.
A 50 kg person travelling in a car going at 70 mph is travelling at 31 m/s. In an emergency, it may take 5 seconds to brake the car.
The acceleration of the car is given by:
= -6.2 m/s2
In order to produce this deceleration on the person of 50 kg, the force required is given by:
= 50 × 6.2
= 310 N