What is the Relationship Between Potential and Kinetic Energy in Physics?

[PhysicsPrac]

Hi,

here is my question:

Potential energy = mgh
Kinetic energy = 1/2mv^2
mgh = 1/2mv^2, solving for v you get v = sqrt(2gh)

Now I know v is the same as dx/dt so if I substite in dx/dt for v :

dx/dt = sqrt(2gh)

Multiply by dt:
dx = sqrt(2gh) * dt
Integrate:
x = t*sqrt(2gh)

This should be right, but for some reason it doesn't work when I check it with the well known x = x0 + v0t + 1/2at^2 formula, what am I doing wrong?

 

[nnnm4]

h is dependent on t, ie it's not a constant. What you calculated is if a ball fell a height h under gravity, and then started moving at constant velocity (at which point you say t=0) then the ball would move x = t*sqrt(2gh) in time t.

 

[PhysicsPrac]

Oh I see, thanks for your help!