# Position Dependent

1. Dec 12, 2008

### homestar2004

A particle moving along the x-axis is acted upon by a resisting force which is such that at a time t for it to travel a distance x is given by t=Ax^2+Bx+C, where A, B, and C are constants. show that the magnitude of the resisting force is proportional to the cube of the instantaneous speed.

I know the chain rule needs to be used and it is just a calculus problem, but I can't seem to start it.

Last edited: Dec 12, 2008
2. Dec 13, 2008

### jdstokes

Start by writing down $dt /dx = \cdots$

3. Dec 13, 2008

### homestar2004

dt/dx= 2Ax+Bx

Now I know I need to get velocity, which is dx/dt, but the only way I can see is to multiply the above by dx/dt, and I don't know if that is right. What about the distance x? Where does it come in?

4. Dec 13, 2008

### Hootenanny

Staff Emeritus
HINT:

$$\frac{dx}{dt} = \frac{1}{\left(dt/dx\right)}$$

You might also want to recheck your derivative.