SOLUTION: I need help with this problem: A particle moves down the x-axis so that its acceleration is given by a(t) = 6t - 2. If its velocity at t = 2 and its position at t = 0 is 2, devel

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Question 1028019: I need help with this problem:
A particle moves down the x-axis so that its acceleration is given by a(t) = 6t - 2. If its velocity at t = 2 and its position at t = 0 is 2, develop the equations which express the particle's position and velocity as a function of t.

Answer by fractalier(6550) About Me  (Show Source):
You can put this solution on YOUR website!
Given a(t), we can integrate to find v(t)...
v%28t%29+=+integral%28a%28t%29+dt%29+=+integral%286t+-+2%29+dt+=+3t%5E2+-+2t+%2B+C%5B1%5D
Now when t = 0, v = 2, so we can find the first constant...
C%5B1%5D+=+2 so that
v%28t%29+=+3t%5E2+-+2t+%2B+2
Now integrate once again to find position...
x%28t%29+=+integral%283t%5E2+-+2t+%2B+2%29+dt+=+t%5E3+-+t%5E2+%2B+2t+%2B+C%5B2%5D
Now when t = 0, x = 2, we have
C%5B2%5D+=+2
and
x%28t%29+=+t%5E3+-+t%5E2+%2B+2t+%2B+2