The problem states that a particle's position at time t is given by the equation:(adsbygoogle = window.adsbygoogle || []).push({});

[tex]x(t)=2\pi t+cos(2\pi t)[/tex]

Therefore, the velocity of the particle at time t would be the first derivative of the above equation:

[tex]x'(t)=v(t)=2\pi-2\pi(sin(2\pi t))[/tex]

I was asked what the maximum velocity of the particle was, and was able to determine that it is 2, but that is only because I used a graphing aid. I am not quite sure where to start on how to find the maximum, other than know what the graph looks like in one's mind's eye, but that seems a little too extreme. I have also calculated the second derivative (acceleration of the particle) if it is needed:

[tex]x''(t)=a(t)=4\pi^2cos(2\pi t)[/tex]

I would show other attempt at work, but we really weren't shown how to do this.

But yes, we still have to do it.

Thank you for your help.

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# Homework Help: Particles and Derivatives

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