Question

An older-model car accelerates from 0 to speed v in a time interval of δt. a newer, more powerful sports car accelerates from 0 to 5v in the same time period. assuming the energy coming from the engine appears only as kinetic energy of the cars, compare the power of the two cars.

Answer 1

Power = Energy / time = Δ kinetic energy / time = ΔKE / t

For old car: ΔKE= m(v^2) / 2 => Power = m(v^2) / (2t)


For new car: ΔKE = m (5v)^2 / 2 => Power = 25 * [ m(v^2) / (2t) ]

Then, comparing the expressions for both cars, you get that the power of the new car is 25 times the power of the old car.