Question

How do we derive the expression for kinetic energy ??

Answer 1

The kinetic energy can be described as the energy supplied or the work done to give velocity to an object.

The work done is given by the product of the force and the distance.

That is kinetic energy can be written as,

`K=F* d\text{ }\rightarrow\text{ (i)}`

From Newton's second law,

`F=ma\text{ }\rightarrow\text{ (ii)}`

Where m is the mass of the object and a is the acceleration of the object due to the applied force F.

From one of the equations of motion,

`v^2-u^2=2ad`

Where v is the final velocity of the object and u is the initial velocity of the object.

Let us assume that the object was at rest initially. Thus, u=0 m/s

Therefore,

`\begin{gathered} v^2=2ad \\ \Rightarrow(v^2)/(2d)=a \end{gathered}`

Substituting the for acceleration in equation (ii),

`F=m*(v^2)/(2d)\text{ }\rightarrow\text{ (iii)}`

On substituting equation (iii) in (i),

`\begin{gathered} K=m*(v^2)/(2d)* d \\ \Rightarrow K=m*(v^2)/(2) \\ \Rightarrow K=(1)/(2)mv^2 \end{gathered}`

Hence the proof.