An older-model car accelerates from 0 to speed v in 10. s. A newer, more powerful sports car of the same mass 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. (Take Pnew and Pold as the powers of the new car and old car, respectively.)

Question

Pnew = Pold

Answer 1

power = work/time
since the time is the same, the power ratio is the work ratio

work in = kinetic energy out

kinetic energy proportional to v^2 [ like (1/2)m v^2 ]

v'^2/v^2 = 16