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

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In summary, to find the power delivered as a function of time, you need to multiply the force and velocity functions. Since they are given as scalar functions, it is implied that all motion and force operate in a single dimension.
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Vitani11
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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!
 

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

What is the difference between P= F(t) • V(t) and P = F • V?

The difference between P= F(t) • V(t) and P = F • V is the inclusion of the variable "t" in the former equation. The variable "t" represents time, and including it in the equation accounts for changes in power over time. On the other hand, the latter equation does not account for changes in power over time, and only calculates the power at a specific moment.

Which equation should I use to find the power done?

It depends on the situation. If you are looking to calculate the power at a specific moment, then P = F • V would be appropriate. However, if you need to account for changes in power over time, then P= F(t) • V(t) would be the better choice.

Can I use either equation for any type of power?

Yes, both equations can be used to find all types of power, as long as the appropriate units are used for force and velocity. For example, if the force is given in Newtons and the velocity in meters per second, the resulting power will be in Watts.

How do I know when to use P= F(t) • V(t) and when to use P = F • V?

If the problem or experiment involves changes in power over time, then P= F(t) • V(t) would be the appropriate equation to use. On the other hand, if the power remains constant or is only needed at a specific moment, then P = F • V would be the better choice.

Can I use these equations interchangeably?

No, these equations should not be used interchangeably as they have different purposes. Using the wrong equation could result in incorrect calculations and inaccurate results.

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