# 2003 AP physics mechanics problem

[SOLVED] 2003 AP physics mechanics problem

Can someone help me figure out the first mechanics problem on the 2003 AP Physics C exam? I'm doing this for review. See post #3 for what I have so far.

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The 100kg box shown above is being pulled along the x-axis by a student. The box slides across a rough surface, and its position x varies with time according to the equation x=.5t^3+2t, where x is in meters and t is in seconds.
a. Determine the speed of the box at time t=0.
b. Determine the following as a function of time t.
i) The kinetic energy of the box
ii) The net force acting on the box
iii) The power being delivered to the box
c. Calculate the net work done on the box in the interval t=0 to t=2s.
d) Indicate below whether the work done on the box by the student in the interval t=0 to t=2s would be greater, less than, or equal to the answer in part c).

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For the first one, find the dx/dt for velocity, find dv/dt for acceleration. Kinetic Energy of box is (1/2)*m*v^2. The net force is the mass of the object times the derived acceleration. The net work is equal to Delta KE, with the initial Kinetic Energy taken at time t=0 (the initial value would be a Constant); Just find dKE/dt and you find the power (it should come down to F*v).

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Here's what I have so far:
dx/dt=1.5t^2+2
dv/dt=3t

a) just plug in 0 for t to find a?
b)
i. 1/2(100kg)(velocity found in a)^2
ii. (100kg)*(3t)
iii. I don't understand. I have to find net work in c, so how can I use that to find delta KE to ultimately find power?
c) Don't understand.
d) once I get b)iii and c) this will be easy.

a is right. For b, i. and ii. are right. For iii., P = F*v. Just multiply the derived velocity with the net force you found in ii. For c), the net work is basically equal to the change in kinetic energy. Your initial Kinetic Energy should have a velocity when t = 0s and your final Kinetic Energy should have a velocity when t = 2s. For d), its asking you whether the work done on the box by student would be larger than the net work, in which the net work includes the effect of friction.

Amaroq Zev, above the list of all the topics, there should be a "New Topic" label. Just click on that to make your post.