# Kinetic Energy

The energy possessed by a body by virtue of its motion is called kinetic energy. The kinetic energy of the body is given as

In vector form,

As

*m*and are always positive, kinetic energy is always positive scalar, i.e., kinetic energy can never be negative.**Kinetic energy depends on frame of reference**The kinetic energy of a person of mass

*m*, sitting in a train moving with speed

*v*, is zero in the frame of train but in the frame of the Earth.

# Workâ€“energy theorem

*dW*

**=**mv**dv****.**Work done on the body in order to increase its velocity from

*u*to*v*is given by

â‡’

Work done = Change in kinetic energy,

*W*= Î”*E*.This is workâ€“energy theorem, it states that work done by a force acting on a body is equal to the change produced in the kinetic energy of the body. This theorem is valid for a system in presence of all types of forces (external or internal, conservative or non-conservative).

If kinetic energy of the body increases, work is positive, i.e., body moves in the direction of the force (or field) and if kinetic energy decreases, work will be negative and object will move opposite to the force (or field).

**Relation of kinetic energy with linear momentum**As we know

So we can say that kinetic energy,

and momentum, P =

From the above relation, it is clear that a body cannot have kinetic energy without having momentum and vice versa.