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.