Two cars are travelling with the same speed and the drivers hit the brakes at the same time. the deceleration of one car is a quarter that of the other. by what factor do the distances required for two cars to come to a stop differ?

The ratio of stopping distances is 4 i.e by a factor 4 the stopping distances differ

Explanation:

Using 3rd equation of motion we have

For car 1

For car 2

Since the initial speed of both the cars are equal and when the cars stop the final velocities of both the cars become zero thus the above equations reduce to

.............(i)

Similarly for car 2 we have

..................(ii)\

Taking ratio of i and ii we get

Let

Thus

The ratio of stopping distances is 4