Question

Find the position and velocity of an object moving along a straight line with the given​ acceleration, initial​ velocity, and initial position. ​a(t) =cos(πt)​, ​v(0)=55​, ​s(0)=77 The velocity is ​v(t)= ____. ​(Type an exact​ answer.)

Answer 1

The initial position has no effect on the velocity, so you can ignore that value (unless there's another part to the question not included, of course).

We have

$v(t)=v(0)+\displaystyle\int_0^t a(u)\,\mathrm du$

$v(t)=55+\int_0^t\cos(\pi u)\,\mathrm du$

$\boxed{v(t)=55+\dfrac1\pi\sin(\pi t)}$