# Work done given force as a function of position

1. Nov 20, 2016

### Thenotsophysicsguy

1. The problem statement, all variables and given/known data
Find the amount of work done between points x1 and x2.
Force at x1: F=ax1
Force at x2: F=ax2
2. Relevant equations
F=ma
W=F (dot product) S
3. The attempt at a solution
W=ax2*(x2-x1)

2. Nov 20, 2016

### Simon Bridge

Welcome to PF;
Is the problem statement exactly as it was written down in front of you?

Guessing this is a 1D problem... so the equation for work comes out as:
$W = \int_{x_1}^{x_2}F(x)\;dx$

Since the force exists only at two points, that means that $F(x)=a\big(\delta(x-x_1)+\delta(x-x_2)\big)$ ... then the integration comes out to 2a or 0 - not sure about when the delta function is right on the limit of the interval. It would depend if that is $x\in (x_1,x_2)$ or $x\in (x_1,x_2]$ or $x\in [x_1,x_2)$ or $x\in[x_1,x_2]$...

Maybe it means that $F=ax$ where a is a constant? Then the integration will work nicely.
Or maybe it is something else.

3. Nov 20, 2016

### Staff: Mentor

Mod note: Please note the change of thread title. It was changed in order to conform with the forum rules and posting etiquette for the homework forums.