# Kinetic energy

## Homework Statement

The speed of a particle doubles and then doubles again because a net external force acts on it. Does the net force do more work during the first or the second doubling? Justify your answer.

## Homework Equations

I'm not sure, but i think E = 1/2 mv(squared)

## The Attempt at a Solution

Im pretty sure this has something to do with kinetic energy, but the question is asking about the net force doing work. How do I incorporate force into this?

olgranpappy
Homework Helper
use the work/kinetic-energy theorem

were you given any values? like mass...etc but i suspect the 2nd doubling because it would require a greater force to accelerate the particle even more than it has already been.

The question asks for how much work the force does. The specifics of the force don't matter, the only thing you want to find is how much work that force does.

Let $$U_{0,1}$$ represent the work done by the force taking it from the initial speed to double the initial speed.
Let $$U_{1,2}$$ represent the work done by the force in taking the particle from double the initial speed to quadruple the initial speed.

To compare $$U_{0,1}$$ and $$U_{1,2}$$, you have to get them both in terms of the same variables. So how can you do this?

I'm not exactly sure how to do that. I think it has something to do with E = 1/2 mv(squared), but that deals with energy and not work. Is this the equation that I should be using when getting U0,1 and U1,2 in terms of the same variables?