A truck, a car and a motor cycle have equal kinetic energies. If equal stopping forces are applied and they stop after a distance of x, y and z respectively, then

1. A truck, a car, and a motorcycle have equal kinetic energies (KE). 2. Equal stopping forces (F) are applied to each. 3. They stop after distances x, y, and z respectively. 4. According to the Work-Energy theorem, the work done by the stopping force equals the change in kinetic energy. 5. Work done (W) = Force (F) × Distance (d). The change in kinetic energy (ΔKE) is from the initial KE to 0 (since they stop). So, ΔKE = 0 - KE = -KE. 6. The work done by the stopping force is negative (as force opposes displacement), so W = -F × d. 7. Therefore, -F × d = -KE, which means F × d = KE. 8. Since the initial kinetic energy (KE) is the equal for all three vehicles, and the stopping force (F) is also equal for all three, the stopping distance (d) must also be equal for all three. 9. Thus, x = y = z.