Kinetic energy is associated with an object in motion. Mathematically, the kinetic energy of an object in motion is given by: K.E. = ½mv^{ 2} where M is the mass of the object in motion, K.E. is the energy (in Joules), V is the velocity of the object in motion. It is important to note that kinetic energy is scalar and that its S.I. units are Joules (J).

When an object is in motion, the work done on the object by a net force is equivalent to the change in kinetic energy of that object: W.D. = K.E._{f} – K.E._{i }where K.E._{f }is the final kinetic energy attained and K.E._{i} is the initial kinetic energy of the object. As taught during our H2 Physics tuition classes, this is also known as the work-energy theorem.

It can also be derived from Newton’s second law of motion as follows:

W = F.s = (ma) s

From the equation (v^{ 2} – v_{0}^{2})/2, we get W = ½ m (v^{ 2} – v_{0}^{2}) = K.E._{f} – K.E._{i}

The following can be noted:

1. If the speed of the object increases, i.e. final velocity (v_{f}) > initial velocity (v_{i}), then the work done is greater than zero (W > 0).

2. If the work done (W) < 0, then the object in consideration is doing work on the agent, exerting the net force.

As all other forms of energy, the kinetic energy also obeys the principle of the conservation of energy. For example, if we consider an object at rest at some height h, then all of its energy is in form of potential energy. When the object falls from its height, it accelerates due to earth’s gravity and the potential energy is transformed into kinetic energy. Finally, when the object reaches the ground (height, h = 0 so potential energy = 0), all of the energy is in the form of kinetic energy and the object is, at this time moving at its maximum velocity.

For an object with a fixed size, the kinetic energy is referred to as the translational kinetic energy of the mass. The object may also possess another form of kinetic energy called the rotational kinetic energy. Therefore the total kinetic energy of an object can is the sum of the translational kinetic energy and the kinetic energy of rotation.

For bodies with speeds comparable to the speed of light, the relativistic kinetic energy equation is used in calculating the kinetic energy of the object.