# On a roller coaster, where does the car have both Kinetic energy and potential energy? Potential energy is related to vertical position and kinetic energy is related to speed or velocity. The roller coaster car has maximum potential energy at the greatest height it reaches and maximum kinetic energy at it's lowest point, where it has maximum speed. At any point between starting from rest and reaching minimum height it will have both potential and kinetic energy. The two forms of energy are equal at a height that's equal to half of the maximum height.

As the car coasts downward its potential energy decreases and kinetic energy increases, then as it heads back up the potential energy increases with height and kinetic energy decreases as it loses speed.

The mathematical relationships are:

Potential energy: PE= mgh

where m=mass of the object, g=9.8 m/s^2 (accleration due to gravity) and h=height.

Kinetic energy: KE=1/2 m(v^2) where m=mass and v=velocity.

Neglecting energy lost to friction and air resistance, you can calculate the speed of the car at any given height if you know its initial height and mass:

KE = inital PE-PE at a given height, or KE = mg[h(initial)-h(final)]

Solve for v using KE = 1/2 m(v^2).

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