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A particle is moving with the given data. Find the position of the particle.

 

a(t) = t^2 − 2t + 6,    s(0) = 0,    s(1) = 20

Guest Apr 1, 2017
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Assuming a(t) is acceleration, then

 

velocity is:  v(t) = t3/3 - t2 + 6t + k1     where k1 is a constant

 

position is:  s(t) = t4/12 - t3/3 + 3t2 + k1t + k2  where k2 is another constant.

 

The two constants are found from:

 

s(0) = 0:    0 = k2

 

s(1) = 20:   20 = 1/12 - 1/3 + 3 + k1 + k2

.

Alan  Apr 1, 2017

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