A car of mass 800 kg is travelling at 30 m/S. The car then brakes suddenly and stops with a braking distance of 75 m find the work done on the car by the brakes

-360 kJ

Explanation:

Given:

m = 800 kg

v₀ = 30 m/s

v = 0 m/s

Δx = 75 m

Find: W

We can solve this using either forces or energy.

To use forces, first find the acceleration.

v² = v₀² + 2aΔx

(0 m/s) ² = (30 m/s) ² + 2a (75 m)

a = - 6 m/s²

Then apply Newton's second law:

∑F = ma

F = (800 kg) (-6 m/s²)

F = - 4800 N

Work is force times distance:

W = FΔx

W = (-4800 N) (75 m)

W = - 360,000 J

W = - 360 kJ

If you want to use energy instead:

work = change in energy

W = ΔKE

W = ½mv² - ½mv₀²

W = ½ (800 kg) (0 m/s) ² - ½ (800 kg) (30 m/s) ²

W = - 360,000 J

W = - 360 kJ