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 4v 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.

Ratio of power produced by new to old car is 16:1

Explanation:

Assuming both cars have the same mass m

Let KE1 and KE2 be the kinetic energies of the old and new car respectively.

v1 = v

and v2 = 4v

KE1 = 1/2mv1² = 1/2mv²

KE2 = 1/2mv2² = 1/2m (4v) ² = 1/2*m*16v² = 8mv²

Ratio of the power produced by the new car to the old one is simply KE2/KE1 = 8mv²/1/2mv² = 16

Since the same time interval is given.