# Finding out maximum from given velocity?

Richard Ros

## Homework Statement

Given that V(t) = π*cos(πt/1.6 + π/6), at which time after t = 0 s is the kinetic energy first at a maximum? The answer is 1.33 seconds. Although, when I put it in the calculator, 1.33s is at a minimum. How would you do this by hand? Step by step work would be appreciated. Thanks!

## The Attempt at a Solution

I was given the position which was x(t) = 1.6 sin(πt/1.6 + π/6) and took the derivative to get V(t) = π*cos(πt/1.6 + π/6). No clue on how to go from there to get to the maximum.

voko
You derivative is not entirely correct. Check that.

But even what you have should be enough to solve the problem. Graph the velocity. You should get a sinusoid. Now graph the kinetic energy. What does it look like?

Richard Ros
I'm pretty sure my derivative is correct as there were more questions to this problem which they asked me the velocity at 0 seconds. As I plugged it in, I got the same answer as the answer key.

voko
Yes, it is correct indeed. Sorry about that. The rest of may message still holds.

Richard Ros
I graphed it but I really want to know how to mathematically determine the maximum or in this case the minimum. Which I think the answer key may of been wrong.

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voko
This is the graph of velocity. What is interesting, is the graph of kinetic energy.

What is the expression for the kinetic energy given the equation for velocity you have found?

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Mentor
The kinetic energy is proportional to v2. For your velocity variation, how do the v2 values at the maxima of v compare with the v2 values at the minima of v? Which occurs first after t = 0, a maximum in v or a minimum in v?