An older model car accelerates from 0 to speed v in 10 seconds. a newer, more powerful sports car accelerates from 0 to 2v in the same time interval. what is the ratio of the average powers expended by the two cars' engines?

For the old car:- By v = u + at =>v = 0 + 10a =>a = v/10 m/s^2 By s = ut + 1/2at^2 =>s = 0 + 1/2 x v/10 x 10 x 10 = 5v Thus F = ma =>F = m x v/10 = mv/10 =>P(old) = F x s = mv/10 x 5v = 1/2mv^2 (i) For new car:- By v = u + at =>6v = 0 + 10a =>a = 3/5v By s = ut + 1/2at^2 =>s = 0 + 1/2 x 3/5v x 10 x 10 =>s = 30v By F = ma =>F = m x 3/5v = 3mv/5 Thus P(new) = F x s = 3mv/5 x 30v = 18mv^2 (ii) =>P(new) : P(old) = 18mv^2 : 1/2mv^2 = 36 : 1