# Homework Help: How to find trajectory as a function of time with energy

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1. Oct 15, 2016

### Cocoleia

1. The problem statement, all variables and given/known data
I am given that an object of mass m has an attractive force F=-A/x^2 acting on it, where A is a constant and x>0. I need to find the potential energy. After i need to suppose initial conditions (x0, v0) such that total energy=0. I need to find the trajectory x(t) with v>0

2. Relevant equations
Potential energy = mgh

3. The attempt at a solution
So far I said that F=ma and then found the acceleration. I integrated the acceleration to find the speed, then I integrated that to find the position, which is A/m ln(x). I said that the potential energy = gAln(x). From this point I am stuck, I can't figure out how to find the trajectory as a function of time.

2. Oct 15, 2016

### Staff: Mentor

F=ma gives you the acceleration as function of distance. Converting this to acceleration as function of time (what you need for the integration steps) is not trivial.
That does not work. This is not a "gravity on a lab scale" setup.
Your position depends on the logarithm of the position?

3. Oct 15, 2016

### Cocoleia

Ok. Then how will I find the potential energy ?

4. Oct 15, 2016

### Staff: Mentor

The definition of potential energy directly gives a way to calculate it based on the force.