The kinetic energy is defined as T = 1/2 mv^{2}. This is the total work done on the particle to bring it from state of rest to a velocity v . The S.I. unit of K.E. is N-m or Joule. K.E. is always positive whether vis positive or negative.

From equation (6.2), we can write

U_{1 -2 }= T_{2} –T_{1}

where T_{2} = 1/2 mv_{2}^{2}

and T_{1} =1/2 mv_{1}^{2}

U_{1-2} = T_{2} –T_{1} = ∆T

Equation {6.3) is the work-energy equation. Equation (6.3) states that total work done

during change of state 1 to 2 is equal to the net change in kinetic energy.

Equation (6.3) can be written as

T_{1} +U_{1-2} = t2

Equation {6.4) states that kinetic energy at state 1 plus the work done during 1 -2

is equal to the kinetic energy at state 2.