Question

A 14,700 N car is traveling at 25 m/s. The brakes are applied suddenly, and the car slides to a stop. The average braking force between the tires and the road is 7100 N. How far will the car slide once the brakes are applied? Using energy analysis?

Answer 1

To find the distance that the car slides once the brakes are applied, we can use energy analysis. We know that the initial kinetic energy of the car is given by:

E_i = 0.5 * m * v^2 = 0.5 * 14700 N * 25 m/s^2 = 148750 J

And the final kinetic energy of the car is zero, since it comes to a stop. The change in kinetic energy is therefore:

ΔE = E_f - E_i = 0 - 148750 J = -148750 J

The work done by the brakes is equal to the change in kinetic energy, so we can write:

W = ΔE = -148750 J

The braking force is given as 7100 N, so the distance that the car slides is given by:

d = W/F = -148750 J / 7100 N = -20.9 m

Therefore, the car will slide a distance of approximately 20.9 meters once the brakes are applied.