Power = Force times Velocity? Really?

Question

Ok, "we can also express the rate at which a force does work on a particle in terms of that force and the particle's velocity".

I'm trying to "see it" conceptually. My primary visualization is that I imagine an x-y coordinate system, x axis is displacement, y is force.

Now I "turn on" the x-axis like a treadmill, and set the treadmill to "5 meters per second" and the x-axis starts going left (i.e. 5 becomes 4, 4 becomes 3, etc...)

Now I "look" at the x-y coordinate system, and draw the Force function onto the graph as if the treadmill were switched off, between the limits of integration.

Now I sorta "visualize" what the result would be if I drew the graph while the X-axis was sliding (treadmill on) but I thought it was off (no sliding).

As a matter of fact, it would be a perfect "stretching" and the effect of the treadmill on the force*distance, is the effect of replacing displacement with velocity in the P=F*V equation! I think I got it!

Answer 1

That visualization seems way too complicated...(but OK if it works for you).

The way I visualize it is to imagine a force acting on a particle for a particular amount of time--say 1 second.

The work done on the particle is Force × the distance it moved.

Power is work/time, so that is:

P = (force × distance) / time

But that's the same as:

P = force × (distance / time)

And since (distance / time) = speed,

P = force × speed

Answer 2

You are overcomplicating it.

Remember that power is a rate of flow, like gallons per minute.

Power is the rate that energy flows, or is used or is generated.

Energy or work is force x distance.

The rate energy is used (power) is energy/time, or force x distance/time.

distance/time is velocity, which leaves Power = F x V

Answer 3

uh, sure dude