Constant power problem

1. May 8, 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, so
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?

2. May 8, 2010

tiny-tim

Hi gaobo9109!

You really only have two unknowns, t and P/m, in your last two equations.

3. May 8, 2010

gaobo9109

but time taken for Object A to travel distance s is given by the equation t = 2s/3v. So my second equation for t should also be expressed in term of s and v so that the two equation can be divided to find the ratio. However, I have P and m in the equation instead. How can I express the second equation in term of s and v?

4. May 8, 2010

tiny-tim

Eliminate P/m from these two equations …