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 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.

Answer 1

Answer:

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.