Calculate the initial and final kinetic energy of the car in the example below.

Question

A car of mass 12100kg is travelling at 15m/s. The driver sees that the traffic light ahead has changed to red and applies the brakes, bringing the car to a stop.

A) Calculate the initial and final energy of the car

B) State the change in kinetic energy as the car comes to a stop

C) The change in kinetic energy is equal to the work done by the brakes in stopping the car. State the work done by the brakes in stopping the car.

D) Given that a force of 18150N was supplied by the brakes of the car, calculate the distance over which the car slowed to a stop.

Answer 1

(A) Kinetic energy is calculated as K = mv²/2 where m is the mass of the object and v is its velocity. The initial kinetic energy is then K₀ = mv₀²/2 = (12100 kg)(15 m/s)²/2 = 1361250 J. Since the car came to a stop, its final velocity is v = 0 and thus it has no kinetic energy. The final kinetic energy is K = 0 J.

(B) The change in kinetic energy, ΔK, is simply ΔK = K - K₀ = 0 J - 1361250 J = -1361250 J.

(C) The change in kinetic energy is equal to the amount of work done. Thus, we take our result from (B) such that W = ΔK = -1361250 J.

(D) We have that the work is equal to the product of the force applied and the displacement over which the force is applied (W = FΔd). Solving the equation for the displacement, we see that Δd = W/F. Taking the work from (C) and the given applied force of F = 18150 N, we see that the car slowed to a stop over a distance |Δd| = |W/F| = |(-1361250 J)/(18150 N)| = |-75 m| = 75 m.