The Time Ratio of Objects A and B with Constant Power: How Do They Compare?

[gaobo9109]

Homework Statement

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

Homework Equations

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

 

[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 :)

Edit: For more info on motion with constant power, see https://kb.osu.edu/dspace/bitstream/1811/2458/1/V30N04_218.pdf

 

[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?

 

[Jolsa]

Indeed.

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