Adriver in a 2144 kg car traveling at 15 m/s hits the brakes, coming to a stop in 67 meters. how far would it take the car to stop if it was instead traveling at 45 m/s?

1) First, let's calculate the value of deceleration a that the car can achieve, using the following relationship:

where S=67 m is the distance covered, vf=0 is the final velocity of the car, and vi=15 m/s is the initial velocity. From this we can find a:


2) Then, we can assume this is the value of acceleration that the car is able to reach. In fact, the force the brakes are able to apply is

This force will be constant, and since m is always the same, then a is the same even in the second situation.

3) Therefore, in the second situation we have a=-1.68 m/s^2. However, the initial velocity is different: vi=45 m/s. Using the same formula of point 1), we can calculate the distance covered by the car before stopping:

As newton's first law states a object in motion stays in motion