P= F(t) • V(t) vs P = F • V to find power done

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The discussion centers on calculating power as a function of time using the equations P = F(t) • V(t) and P = F • V. The force F(t) and velocity V(t) are provided as functions of time, leading to the question of whether to multiply or dot them. It is clarified that since both are scalar functions in a single dimension, they should simply be multiplied. The conclusion emphasizes that the scalar nature of the functions allows for straightforward multiplication to find power over time. Understanding this approach simplifies the calculation of power in this context.
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Homework Statement


What is the power delivered as a function of time?

F(t) = m(12t-8)
V(t) = (6t^2-8t)

Homework Equations


P = FV vs. P = F • V

The Attempt at a Solution


I'm given a force and velocity as functions of time. When I find power, do I multiply or dot them? I know you should dot when force and velocity are defined vectors, but here they are generalized and not represented by vectors but actually by functions.
 
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Just multiply them. If they are given as scalar functions rather than vectors, it is implicit that all motion and force operates in a single dimension.
 
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andrewkirk said:
Just multiply them. If they are given as scalar functions rather than vectors, it is implicit that all motion and force operates in a single dimension.
Right... these are only in terms of a single dimension and vary with time - I don't know what was going on with my brain there. Thanks!
 

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