How Do You Calculate Position from Velocity at Time t?

[karush]

$\tiny{205.o27.12 }$
$\text{Given the velocity $v=\frac{ds}{dt}$}$
$\text{and the initial position of a body moving along a
coordinate line,}$
$\text{find the body's position at time t}$
\begin{align}
\displaystyle
v&=\sin\left({\pi t}\right) &s(0)&=20 \\
v'&=\cos{(\pi t)} \\
s(t)&=
\end{align}
$\text{lost.. } $

 

[Greg]

I think it's like this:

$$s(t)=\int\sin(\pi t)\,\text{d}t=-\frac1\pi\cos(\pi t)+C$$

$$s(0)=-\frac1\pi+C=20\implies C=20+\frac1\pi$$

$$s(t)=-\frac1\pi\cos(\pi t)+20+\frac1\pi$$

 

[karush]

so $$s'(t)=v(t)$$

;)