# Physics - power and motion

1. Oct 21, 2009

### deathnote93

[SOLVED] Physics - power and motion

1. The problem statement, all variables and given/known data 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 t3/2

2. Relevant equations
P = F.v

F = dp/dt, p=mv

v = dx/dt

3. 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?

Last edited: Oct 21, 2009
2. Oct 21, 2009

### Troels

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 :)

Last edited: Oct 21, 2009
3. Oct 21, 2009

### 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!