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?
Answer:
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
