Question

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

Answer 1

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