Antonia Boomershine: now that you mention newtons second law, i think that must be the way we are meant to work it out, not with kinetic energy. can anyone please explain it that way?thankyou very much for your answer though, i really appreciate it!
Lewis Ranft: You could do it by considering Newton's Second Law (the whole F=ma thing), but I think it'll be easier to look at it from an energy/power standpoint. If car B has an engine three times as powerful, it transfers energy three times as fast. Remember - power is the rate of doing work or using energy. So, in the same amount of time, car B will end up with three times the kinetic energy as car A (ignoring friction and the like). How does that translate to speed? Kinetic energy is half the mass times the square of the speed. Let T be the kinetic energy, then for car A:T = (1/2)m v^2For car B,3T = (1/2) m v'^2where v is car A's speed and v' is car B's.Plug in:3(1/2)m v^2 = (1/2)m v'^2The (1/2) and the m drop ! out3 v^2 = v'^2sov' = v sqrt(3)So, in the same period of time, car B will reach a speed sqrt(3) times that of car A. If we make the simplifying assumption that they started from rest and then calculate the acceleration, we can see that the acceleration of car B will be sqrt(3) times that of car A - about 1.7 times....Show more
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