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### Position Function of a Moving Particle

```
Date: 9/9/96 at 14:15:46
From: Anonymous
Subject: Position Function of Particle Moving at....

A particle moves on a straight line with a velocity fxn
v(t)= sin(w)cos^2wt.  Find its position fxn s=f(t) if f(0)=0.
Note that w is a constant.

How would I even approach this problem?
Any assistance would help,

Thanks,
Al
```

```
Date: 9/9/96 at 23:0:45
From: Doctor Jerry
Subject: Re: Particle Motion

Use the fact that the derivative of the position function is the
velocity function, that is, f'(t) = v(t).  All you have to do is to
determine, by integration, a function whose derivative is
sin(w)*cos^2 (wt).  Once you find such a function, note that you can
add to it any constant.  This won't change the fact that its
derivative is sin(w)*cos^2 (wt).  Choose the constant so that
f(0) = 0.  That's it.  Not too bad.

The sin(w) is a constant, so all you have to integrate is cos^2(wt).
For this use the identity cos^2 (A) = (1+cos(2A))/2.

I hope this gets you started.

-Doctor Jerry,  The Math Forum
Check out our web site!  http://mathforum.org/dr.math/
```
Associated Topics:
High School Calculus

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