- #1

- 5

- 0

**This is not so much coursework as it is a thought experiment that has been bugging me for a while now.**

1. Homework Statement

1. Homework Statement

Find the equation for velocity either as a function of distance (x) or time (t).

I have an object whose acceleration is given by the rational function a(x) = (a+x)/(b-x) where x is the distance traveled and a and b are some constant.

The actual equation has many more values and constants in it but this simplified version should be fairly similar.

**2. The attempt at a solution**

First, I resorted to the motion equations but quickly realized that the acceleration is not constant. My second thought was to use motion equations that deal with variable acceleration that use jerk and so forth but soon found that due to the rational nature of the function a(x) that it is not possible to get a derivative that is a constant.

Yesterday, the idea came to me that if I took the derivative of a(x) my resulting function would have the units 1/(sec)

^{2}which could be manipulated by taking the square root of the reciprocal to obtain time with respect to distance (x). However, this still does not solve the problem because I'm not sure if the manipulation is mathematically sound and this still does not solve the problem of variable acceleration. Any thoughts?