Acceleration and curvature (1 Viewer)

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1. The problem statement, all variables and given/known data

Show that this statement is false: when a moving particle along a curve reaches its max. speed at t=3, its acceleration is 0.

2. Relevant equations

a = d^2 R / dt^2 = d|v|/dt * T + k |v|^2 N

where k = |dT/ds|, T = v/|v|, N = 1/k dT/ds

3. The attempt at a solution

|v| is max at t = 3 so it is nonzero so the second term in acceleration should be nonzero and hence a nonzero total acceleration will result. I think the first term could, however, be 0 since the derivative of the speed will be 0 at this point. Is this correct? Is there a proper way to show this?
 

Dick

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Sure. N could be a nonzero vector. So even if the tangential acceleration is zero it could have a normal component. The problem only asks you to show that it's false. All you need is a counterexample. Almost anything would work. Like circular motion at a nonuniform velocity.
 

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