How Does Constant Power Affect Object Motion Compared to Constant Force?

[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, 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?

 

[tiny-tim]

But how do i eliminate m and p?

Hi gaobo9109!

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

 

[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?

 

[tiny-tim]

Eliminate P/m from these two equations …

Object B has constant power, so
…
3/2 mv² = Pt
…
s = 1/3 (8Pt³/9m)^1/2