Finding Kinetic Energy from graph of Power

[mintsnapple]

Homework Statement

Homework Equations

P = dW/dt
Change in work = Change in Kinetic Energy

The Attempt at a Solution

Since the integral of the power graph is work done in the system, and since it starts at 0, does this mean kinetic energy is the same thing? So I can probably make a triangle with a height of 20 and base 1 to get an area of 10 for the first problem? And then 30 for the next one?

Though I feel this is much more complicated than that...

 

[haruspex]

I can probably make a triangle with a height of 20 and base 1 to get an area of 10 for the first problem? And then 30 for the next one?

Yes, except that they are clearly not triangles. Can you think of a nonlinear equation that might better represent those curves?

 

[mintsnapple]

Yes, except that they are clearly not triangles. Can you think of a nonlinear equation that might better represent those curves?

The question says estimate, so would an equation for the curve be necessary?

Also, one of the tutors explicitly said there were two things to the Work Energy Theorem:
1. The net work on a system is equal to the change in total energy of
that system.
2. The net work on a structureless element of a system is equal to the
change in kinetic energy of that element.

My concern: Does potential energy play any part in this problem?

 

[haruspex]

The question says estimate, so would an equation for the curve be necessary?

Also, one of the tutors explicitly said there were two things to the Work Energy Theorem:
1. The net work on a system is equal to the change in total energy of
that system.
2. The net work on a structureless element of a system is equal to the
change in kinetic energy of that element.

My concern: Does potential energy play any part in this problem?

The question is really much too vague. If you allow for the possibility that some of the power has gone into potential energy (e.g. pushing it against a strong electric field) then all you can hope to do is provide an upper bound on the KE.
Since it doesn't say how accurate the estimate is to be, yes, you could just treat the curve as a sawtooth, but by the same argument you could just estimate 0.
So we are left to guess what is wanted. My guess would be to approximate the curves as either sine or negative quadratic.