# Calculus

A particle is moving with the given data. Find the position of the particle.
a(t) = 2t + 5, s(0) = 2, v(0) = −4
s(t) = ?

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1. a(t) = 2t + 5
v(t) = t^2 + 5t + c
given: when t=0 velocity = -4
-4 = 0 + 0 + c
c = -4, so
v(t) = t^2 + 5t - 4
s(t) = (1/3)t^3 + (5/2)t^2 - 4t + k
when t = 0, s(0) = 2
2 = 0 + 0 + 0 + k, so k = 2, and finally

s(t) = ......

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2. Hummm, looks a lot like the Allison problems down below.

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