# Constant power question

1. May 6, 2010

### gaobo9109

1. The problem statement, all variables and given/known data
Object A of mass m is pushed with a constant force, another object B of the same mass is pushed with a force that does work at constant rate. Velocity of both objects increase from v to 2v and they move a distance of s. Find the ratio of the time taken by objects A and B to move the distance s

2. Relevant equations

3. The attempt at a solution
Firstly, for object A
s = 1/2(v + 2v)t
t = 2s/3v

Object B has constant power, thus
F1v = F2(2v)
But I don't know how to find an expression for the time taken by object B in term of v and s

2. May 6, 2010

### Jolsa

Use energy considerations.

First: What is the total change in energy?

Second: Find the velocity as a function of P and t and integrate this to obtain the position as a function of time.

Now you can use these to equations to eliminate P.

Good luck :)

3. May 7, 2010

### gaobo9109

change in energy = work done = 3/2 mv2
3/2 mv2 = Pt
v = (2Pt/3m)1/2
integrating this term, i get
s = 1/3 (8Pt3/9m)1/2

But how do i eliminate m and p?

4. May 9, 2010

### Jolsa

Indeed.

Try looking at the first equation again. Can't you use that to eliminate the ratio P/m?