1. ## Position Function Question

Here is the question:

If the velocity function for a projectile is v(t) = 4 cos ( t), which of the following is a possible corresponding position function?

Could someone explain this to me? Thanks

2. Hello vease1999
Originally Posted by vease1999
Here is the question:

If the velocity function for a projectile is v(t) = 4 cos ( t), which of the following is a possible corresponding position function?

Could someone explain this to me? Thanks
$v = \frac{ds}{dt}=4\cos(\pi t)$

$\Rightarrow s = \int4\cos(\pi t)\,dt$
$=\frac{4}{\pi}\sin(\pi t) + c$
So if the initial conditions are such that $c = \frac{8}{\pi}$, the solution would be:
$s = \frac{8+4\sin(\pi t)}{\pi}$

3. I was wondering if I could get a little more explanation on this. You'll have to bear with me. I'm pretty much at level 0. Thanks.

4. Hello vease1999

Velocity is the rate of change of position.
$v = \frac{ds}{dt}=4\cos(\pi t)$
So we integrate to find s.
$\Rightarrow s = \int4\cos(\pi t)\,dt$
Do you know how to integrate the cosine function?
$=\frac{4}{\pi}\sin(\pi t) + c$
c can have any constant value; for example $\color{red}\frac{8}{\pi}$.
So if the initial conditions are such that $c = \frac{8}{\pi}$, the solution would be:
$s = \frac{8+4\sin(\pi t)}{\pi}$