A 1210 kg rollercoaster car is moving 7 33 m/s. As it approaches the station, brakes slow it down to 1.88 m/s over a distance of 5.29 m. How much work did the brakes do

Answer 1

Write Initial Kinetic Energy as .5mv_i² = .5 × 1210 kilograms times (7.33 meters per second)² or 32505.9845 Joules.

Write Final Kinetic Energy as .5mv_f² = .5 × 1210 kilograms times (1.88 meters per second)² or 2138.312 Joules.

.5mv_f² − .5mv_i² gives -30367.6725 Joules of Work or Kinetic Energy required by the brakes to slow the car from 7.33 meters per second to 1.88 meters per second over the distance of 5.29 meters. The negative sign in -30367.6725 Joules indicates that the Work is opposite or against the direction of the car as it "bleeds" or reduces the car's speed.