The acceleration of the car is  ft/s².

The acceleration of the object is , where  is the velocity.

Hence .

The antiderivative of  is

, where  is the constant.

Initial velocity of the car is  mi/h.

Substitute  and  in .

Therefore the velocity of the car is .

When brakes are applied then car comes to rest position, .

After s car comes to rest position.

The velocity of the object is , where  is the distance.

Hence .

The antiderivative of  is

, where  is the constant.

Initial distance is .

Therefore the distance of the car at time  is .

Find the velocity when car comes to rest position.

The distance travelled by the car is  ft.

After s car comes to rest position.

Substitute  and  in .

Therefore the velocity of the car traveling when brakes were applied is  ft/s.

The velocity of the car traveling when brakes were applied is  ft/s.