Need, quick answer, please Energy integral/derivative

[briteliner]

Homework Statement

Start from this equation: E=(1/2)mv_r^2+U(r)

and solve for dt. Set up the integral to find the relation between r and t, then carry out the integral in the special case that E=0.

Homework Equations

The Attempt at a Solution

HOW DO I GET DT? DO I HAVE TO TAKE THE DERIVATIVE OF THIS? IF SO, WITH RESPECT TO WHAT?

THANKS!

 

[rootX]

Homework Statement

Start from this equation: E=(1/2)mv_r^2+U(r)

and solve for dt. Set up the integral to find the relation between r and t, then carry out the integral in the special case that E=0.

Homework Equations

The Attempt at a Solution

HOW DO I GET DT? DO I HAVE TO TAKE THE DERIVATIVE OF THIS? IF SO, WITH RESPECT TO WHAT?

THANKS!

t is time, and I assume you are trying to prove that energy remains constant using vector calculus. v = dr/dt.

 

[briteliner]

i understand that dt is time, but now how to get dt.

 

[rootX]

I told you v = dr/dt.

I never went through all of this derivation, but I think that's the only dt there.