A particle has an acceleration given by a(t)=2sin(4t) for t>0. let v(0)= -2 and s(0)=1. find the velocity and

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A particle has an acceleration given by a(t)=2sin(4t) for t>0. let v(0)= -2 and s(0)=1. find the velocity and

[From: ] [author: ] [Date: 12-08-31] [Hit: ]

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Position functions. How do we find these given values on their graphs?

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v(t) = ∫2sin(4t) dt = -1/2*cos(4t) + C => -2 = -1/2 + C => C = -3/2

v(t) = -1/2*cos(4t) - 3/2

s(t) = ∫v(t) dt = -1/8*sin(4t) - 3t/2 + D

D = 1

s(t) = -1/8*sin(4t) - 3t/2 + 1

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v(t) = ∫a(t) dt

s(t) = ∫v(t) dt

Go from there.

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