Work done by General Variable force

[1MileCrash]

Homework Statement

The force on a particle is directed along an x-axis and is given by F = F₀(x/x₀ - 1).

Find the work done by the force in moving the particle from x = 0 to x = 2x₀

Homework Equations

The Attempt at a Solution

It looks like the force is a recurrence relation or something...

$W = \int^{2x_{0}}_{0} F_{0}(x/x_{0}-1) dx$

I don't really understand.. unless I just take x₀ to be the lower limit of integration, 0, and then 2x₀ is just also 0, leaving me integrating from 0 to 0... which is just 0, but that seems to render this an absurdly stupid question.

 

[ehild]

F₀ and x₀ are undetermined constant.

ehild

 

[1MileCrash]

So x0 is could not be described as lower limit of integration? I see it as integrating from original x position to two times original x position, which in this case is 0 to 0, which means the integral is 0?

How do you view it?

 

[ehild]

So x0 is could not be described as lower limit of integration? I see it as integrating from original x position to two times original x position, which in this case is 0 to 0, which means the integral is 0?

How do you view it?

X₀ is just a number and the upper limit of integration is 2X₀, the lover limit is zero.

Yes, the integral is 0. The antiderivative is F₀(x²/(2x₀)-x), which returns 0 between the limits.

ehild