Given the velocity v=ds/dt and the initial position of a body moving along a coordinate line, find the body's position at time t. v=sin(pi*t), s(-3)=0

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19-11-2016
Mathematics

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Given the velocity v=ds/dt and the initial position of a body moving along a coordinate line, find the body's position at time t. v=sin(pi*t), s(-3)=0

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nobillionaireNobley nobillionaireNobley · Answer 1 · 2016-11-21T20:27:56+01:00

nobillionaireNobley nobillionaireNobley

21-11-2016

s(t) = ∫vdt = ∫sin(πt)dt = (-cos(πt))/π + c
s(-3) = (-cos(-3π))/π + c = 0
(-cos(3π))/π + c = 0
1/π + c = c
c = -1/π

Therefore, s(t) = (-cos(πt))/π - 1/π = (-cos(πt) - 1)/π

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