How does the distance a car travels before coming to rest relate to its speed when brakes are applied?

The relationship between the distance a car travels before coming to rest and its speed when the brakes are applied is best described by the principle that the stopping distance is proportional to the square of the speed. This is derived from the physics of motion and specifically from the equations of uniformly accelerated motion.

When a car is decelerating due to braking, the kinetic energy of the car is being converted into work done against the braking force. The kinetic energy of a moving object is given by the formula ( KE = \frac{1}{2}mv^2 ), where ( m ) is the mass of the car and ( v ) is its speed. When a car comes to a stop, all that kinetic energy must be dissipated by the brakes.

The work done by the brakes on the car to bring it to rest is equal to the force applied multiplied by the stopping distance (work = force × distance). This means that if a car travels a longer distance to stop, more work must be done, which corresponds to a greater initial kinetic energy due to a higher speed. When you set the initial kinetic energy equal to the work done by the brakes, you will discover that the stopping distance depends on the square of the initial speed.

Therefore