How are potential and kinetic energy different from each other?

Answer 1

Potential and Kinetic energy relate to position and motion, in that sense Kinetic denotes motion and Potential denotes position. Energy is energy in both cases. There is however a deeper difference between them when it is realized that energy is a quaternion consisting of real or scalar energy and vector energy.

Physics consdiers energy a derivative of work and as such is real or scalar as in W=F.D or work =FDcos(x) this is mathematically a scalar. In short physics considers energy a scalar with units joules or newton meter (Nm). However, FxD=FDsin(x) has the same units as energy joule or Nm but it is not called energy it is called Torque and is a vector.

This distinction between scalar or real energy and vector energy is significant and is the real distinction between potential and kinetic energy. Kinetic energy is a form of vector energy characterized by Ev= mcV where V is a vector. I use V to distinguish it from v the scalar value of V, v= |V|.

Much more could be said but kinetic energy is a form of vector energy.

Answer 2

Kinetic energy is the form of energy that an object has by reason of its motion.

The kind of motion may be translation (motion along a path from one place to another), rotation about an axis, vibration, or any combination of motions. The total kinetic energy of a body or system is equal to the sum of the kinetic energies resulting from each type of motion. The kinetic energy of an object depends on its mass and velocity.

Whereas, potential energy is the energy stored by an object by virtue of its position.

For example, an object raised above the ground acquires potential energy equal to the work done against the force of gravity; the energy is released as kinetic energy when it falls back to the ground. Similarly, a stretched spring has stored potential energy that is released when the spring is returned to its unstretched state.