U(x) + K(x) = Etotal = constant
K(x) = 1/2 mv2 = Etotal - U(x)
Suppose we take one of the potential energy curves from the previous page and put it on a graph of total energy versus position as shown: Since the total energy is a constant, the kinetic energy K must vary as a function of position. The turning points of the motion occur when K = 0. Consider one dimension motion in the x-direction without friction.
U(x) + K(x) = Etotal = constant
K(x) = 1/2 mv2 = Etotal - U(x)
So K(x) = 0 and v = 0 whenever Etotal = U(x).
The turning points occur when K = 0 near x = 0.6 and 7.0, and the maximum speed occurs at x =3.9.