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Suppose you push a hockey puck of mass m across frictionless ice for a time delta t, starting from rest, giving the puck speed v after traveling distance d . If you repeat the experiment with a puck of mass 2m.How long will you have to push for the puck to reach the same speed ? How long will you have to push for the puck to travel the same distance d?I thought it was 2t but it's not... I have tried everything but I can't seem to get the right answer. The answer does not depend on a, t, delta t (I have tried values with these variables and I got " The answer does not depend on _____" Thanks!!!P

Mina Herzog · Accepted Answer

What you left out, it the force you use to push the two pucks. Are they the same, or different?Assuming they are the same magnitude force, then, from F=ma, the second one will have half the acceleration. a) Half the acceleration, means to reach the same speed, from a = v/t ort = v/awith half the acceleration that becomes t = v/(a/2) = 2v/aComparing the two, the second time is twice of the first to reach the same speed (a)b) Half the acceleration, means to reach the same distance, from d = ½at² ort = √(2d/a)with half the acceleration that becomest = √(2d/(a/2)) = √(4d/a) = 2√(d/a)dividing the two times, that is Δt = [ √(4d/a) ] / [ √(2d/a) ] = √2the second time is √2 of the first, or 1.4 times longer to reach the same distance (b).

Lavinia Carroll

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