Position Function Question

**vease1999** · April 26th 2010, 06:54 AM

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?

Here is the answer:

Could someone explain this to me? Thanks

**Grandad** · April 26th 2010, 07:07 AM

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?

Here is the answer:

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:

$s = \frac{8+4\sin(\pi t)}{\pi}$

Grandad

**vease1999** · April 26th 2010, 03:14 PM

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.

**Grandad** · April 26th 2010, 10:26 PM

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:

$s = \frac{8+4\sin(\pi t)}{\pi}$

Grandad

Thread: Position Function Question