Question

Given the velocity v=ds/dt and initial position of a body moving along a coordinate line, find the body's position at time t. v = sin(pi(t)) s(-6)=0.

Answer 1

Given the velocity v=ds/dt and initial position of a body moving along a coordinate line, find the body's position at time t. v = sin(pi(t)) s(-6)=0.

Answer 2

\[\int\limits_{a}^{b} v(t) = s(t) = -(1/\pi)*\cos(\pi(t))+C\]

s(t)=0 at t=-6 so C=(1/pi)
So finally,
\[s(t)=[-\cos(\pi*t)+1]/\pi\]

Answer 3

Thanks.