What is Kinetic Energy?

Many problems in physics require an application of kinetic energy. Kinetic energy is a form of energy that represents the energy of motion. It is a scalar quantity, which means it has a magnitude but not a direction. It is, therefore, always positive (as will be evident when we see the equation that defines it).

Deriving Kinetic Energy

Kinetic energy is closely linked with the concept of work, which is the scalar product(or dot product) of force and the displacement vector over which the force is applied.

Using some basic kinematics equations, we obtain an equation for the acceleration of an object which changes speed. (In the following equation, the term x - x0 has been replaced by s, a term which represents the total distance of displacement.)

v2 = v02 + 2as

therefore,

a = ( v2 - v02 ) / 2s

Applying Newton's Second Law of Motion, F = ma, we get:

F = ma = m ( v2 - v02 ) / 2s

and, multiplying by the distance s (for work) and breaking it apart, we get:

W = Fs = 0.5mv2 - 0.5mv02

 The kinetic energy, K (or sometimes Ek) is, therefore, defined as:

K = 0.5mv2

It should be noted that, as mentioned before, this quantity will always be a non-zeroscalar quantity. If the object has mass and is moving, it will always be positive. It will be zero in the case of a massless object or an object at rest (zero velocity). Thekinetic energy equation, therefore, gives us no information about the direction of the motion, only about the speed.

Work-Energy Theorem

The work-energy theorem comes from the above derivation, and indicates that the work done by an external force on a particle is equal to the change in kinetic energy of the particle. Mathematically, then, you get:

Wtot = K2 - K1 = delta-K

Using Kinetic Energy

In addition to obtaining the work done, the kinetic energy equation is used frequently in conjunction with other forms of energy. Due to the law of conservation of energy,we know that the total energy in a closed system will remain constant. Therefore, analyzing the kinetic energy along with, say, gravitational potential energy allows us to figure out certain factors of the motion. (For an example of this, see the Free Falling Body problem.)