(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

In the engine, a 7-inch rod is fastened to a crank of radius 5 inches. The crankshaft rotates counterclockwise at a constant rate of 200rpm. Find the velocity of the piston at t=1/1200min.

2. Relevant equations

θ = 400πt

[itex]\frac{dx}{dθ}[/itex] = -5sinθ - [itex]\frac{25sinθcosθ}{\sqrt{24 + 25cos^{2}θ}}[/itex]

3. The attempt at a solution

[itex]\frac{dθ}{dt}[/itex] = 400π

[itex]\frac{dx}{dt}|_{t=\frac{1}{1200}}[/itex] = -5sin[itex]\frac{π}{3}[/itex]θ' - [itex]\frac{25sin\frac{π}{3}cos\frac{π}{3}θ'}{\sqrt{24 + 25cos^{2}\frac{π}{3}}}[/itex]

[itex]\frac{dx}{dt}|_{t=\frac{1}{1200}}[/itex] = (-6.30)*(400π)

[itex]\frac{dx}{dt}|_{t=\frac{1}{1200}}[/itex] = -7917in/min

EDIT: Okay, so I think I fixed the main problem (I wasn't accounting for θ' in the equation with respect to time). I would really appreciate a check on my answer, though (this is an extra credit question that could boost my calc 1 grade up from a B to an A). Also, the maximum velocity should logically be at π/2 (correct?) but at π/2 (with respect to angle), I only come up with -5 for x'. Can anyone explain this?

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# Velocity of a Piston

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