Finding out maximum from given velocity?

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Homework Help Overview

The discussion revolves around determining the time at which kinetic energy is maximized based on a given velocity function, V(t) = π*cos(πt/1.6 + π/6). The original poster expresses confusion regarding the relationship between the velocity function and kinetic energy, particularly noting a discrepancy between their calculations and the provided answer key.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the original poster's derivative of the position function and its implications for finding maxima of kinetic energy. There are inquiries about the graphical representation of velocity and kinetic energy, and questions about the relationship between the maxima and minima of the velocity function.

Discussion Status

The discussion is ongoing, with participants exploring different interpretations of the problem. Some guidance has been offered regarding graphing the functions involved, and there is an acknowledgment of the original poster's derivative as correct. However, there remains uncertainty about the relationship between the velocity and kinetic energy maxima.

Contextual Notes

Participants are working under the assumption that the answer key may contain an error, and there is a focus on understanding the mathematical determination of maxima and minima without providing explicit solutions.

Richard Ros
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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!

Homework Equations





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.
 
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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?
 
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.
 
Yes, it is correct indeed. Sorry about that. The rest of may message still holds.
 
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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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?
 
Last edited:
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?
 

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