How to Calculate Time for Particle Movement in 1D with Potential Energy?

[ross_inc]

Homework Statement

Equation for a particle moving in one dimension with potential energy U(x):

t=$$\int$$1/$$\sqrt{2(E-U(x))/m}$$ , integrated from x0 to 5x0

Suppose U(x)=c/x for x>0. Calculate the time for the particle to move from x0 to 5x0, starting from rest at x0. Leave the answer in terms of m,c,x0

Homework Equations

E=mv²/2-U(x)

U(x)=c/x for x>0

The Attempt at a Solution

I've been working on this for a few hours, subbing E and U(x) out will give an integral w/ a denominator of:

$$\sqrt{2(mv²/2-2c/x)/m}$$

however that now puts a v into the mix and it specificaly says "solve in terms of m,c, x0". Should i be replacing v with an equation for velovity or somthing? this integral is getting way nasty.

 

[proby18]

hey, I have this exact same problem, how does one do this?