What is the stopping distance if the car is initially traveling at speed 5.0v? assume that the acceleration due to the braking is the same in both cases?

The question seems to be expecting a comparative answer.

Let us consider Scenario 1 first.

We have the variables listed as follows:

Initial Velocity   = v m/s

Final Velocity   = 0, since the car is stopping.

Acceleration  = - a   , since the car is slowing down.

Let the stopping distance in this case be S

We can arrive at the expression for S by using the equation

Plugging in what we know, we get

Hence, stopping distance in Scenario 1 is

Now, considering Scenario 2, we have

Initial Velocity = 5v m/s

Final Velocity   = 0

Acceleration  = - a  , since it is given to be same in both the cases.

Let the stopping distance this time be

We can use the same equation for this scenario too, i.e.

Plugging in what we have, we get

Solving this for  , we get

This can be written in terms of S as

Thus, the car's new stopping distance will be 25 times compared to the older one!

car stops. he keeps going = he has inertia

a and b sometimes have a positive value