Solving Power Equation & Compressing a Spring: A Step-by-Step Guide

[ACLerok]

I'm having trouble with one problem. The question aske me to finf the amount of power from the equation I found for work. Here is the equation for work: W=F*v*t*cos(theta) I am supposed to come up with an equation that will tell me how much power this is using the variables in the equation. A friend told me to take the derivative but I'm nto sure how to. How do i go about this?

Oh and this as well:
To stretch a spring a distance x_1 from its unstretched length, an amount of work of W must be done.

How much work must be done to compress this spring a distance x_2 from its unstretched length?

 

[lastlaugh]

power is work/time
that should be a pretty good hint

 

[HallsofIvy]

Knowing the definition of "power" would be extremely useful in doing any problem about power! Are you sure that you do?

Oh and this as well:
To stretch a spring a distance x_1 from its unstretched length, an amount of work of W must be done.

How much work must be done to compress this spring a distance x_2 from its unstretched length?

You need to know either:
that the formula for work done in either compressing or stretching a spring a distance x is (1/2)kx² where k is the spring constant and x is the distance stretched or compressed or
(what follows immediately from that formula)
that the work done in compressing or stretching a spring a distance x is proportional to x².

IF W is the work done stretching the spring a distance x_1 and W_2 is the work done in compressing it a distance x_2, then
W/(x_1)²= W_2/(x_2)²(= (1/2)k) so that

W_2= (x_2/x_1)² W_1