Thread: 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?

Here is the answer:



Could someone explain this to me? Thanks

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

$\displaystyle v = \frac{ds}{dt}=4\cos(\pi t)$

$\displaystyle \Rightarrow s = \int4\cos(\pi t)\,dt$

$\displaystyle =\frac{4}{\pi}\sin(\pi t) + c$

So if the initial conditions are such that $\displaystyle c = \frac{8}{\pi}$, the solution would be:

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

Grandad

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.

Hello vease1999

Velocity is the rate of change of position.

$\displaystyle v = \frac{ds}{dt}=4\cos(\pi t)$

So we integrate to find s.

$\displaystyle \Rightarrow s = \int4\cos(\pi t)\,dt$

Do you know how to integrate the cosine function?

$\displaystyle =\frac{4}{\pi}\sin(\pi t) + c$

c can have any constant value; for example $\displaystyle \color{red}\frac{8}{\pi}$.

So if the initial conditions are such that $\displaystyle c = \frac{8}{\pi}$, the solution would be:

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

Grandad