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Old Sep 22nd 2014, 11:35 AM   #1
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Phys Mechanics Kinematics

A block is attached to the wall by some complicated spring-like device. It starts at the point x=A at time t=0 moving to the right with a velocity whose magnitude varies with time according to v(t)=c1t-c2t^2 where c1 and c2 are known constants. How far will it travel before starting back to left?

Please help, I thought you would just take the integral of v(t)=c1t-c2t^2 and that gave me x(t)= c1t^2/2 -c2t^3/3 +A but the answer is x(t)=1/6 c1^3/c2^2 +A
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Old Sep 22nd 2014, 12:21 PM   #2
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You are half way there. You have an equation for position as a function of time, but you haven't yet figured out what the value of t is. The object starts to move backward when v(t) = 0. Come up with that value, then substitue in for t in your equation and you shoud get the answer.
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Old Sep 22nd 2014, 12:58 PM   #3
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Okay I am not sure I really understand. Do you mean 0=c1t-c2t^2 and solve for t then plug that number (c1/c2) into the x(t) equation for t?
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Old Sep 22nd 2014, 01:04 PM   #4
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Originally Posted by NSB3 View Post
Okay I am not sure I really understand. Do you mean 0=c1t-c2t^2 and solve for t then plug that number (c1/c2) into the x(t) equation for t?
Precisely.
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