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/
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