Understanding the Relationship Between Power and Motion in Physics

[deathnote93]

[SOLVED] Physics - power and motion

Homework Statement

A body is moving in a straight line under the influence of a source of constant power. Show that its displacement in time t is proportional to t^3/2

Homework Equations

P = F.v

F = dp/dt, p=mv

v = dx/dt

The Attempt at a Solution

Absolutely no idea where to begin, sorry. I'm not even sure what 'source of constant power' means here - is the force constant or the velocity?

 

[Troels]

The Attempt at a Solution

Absolutely no idea where to begin, sorry. I'm not even sure what 'source of constant power' means here - is the force constant or the velocity?

First it helps to notice that the motion is one-dimensional; so you can drop the vectors.

Unlike motion under constant force, motion under constant power is not uniformly accelerating, because it takes more and more energy to achieve the same velocity increase. Neither the Force nor the velocity are constant in time, but their product is.

You must have, in other words:

$$F(t)v(t)=P_0$$

where P₀ is a constant. Inserting $$F=m dv/dt$$, you get:

$$mv(t)\frac{dv(t)}{dt}=P_0$$

Which is a seperateable ODE which gives you v which can then be integrated to give x.

Good luck and Have Fun :)

 

[deathnote93]

Ah, using integration was the last thing on my mind when I was trying this problem in my head.

Got it now, thanks a LOT!