Question

Define kinetic enery and derive the formula

Answer 1

The energy Wich an object has because of it's motion is called it's kinetic energy.

Answer 2

$\huge{ANSWER}$

◼$\underline \bold {KINETIC ENERGY }$

▶The energy possessed by a body due to its rest state of motion is called kinetic energy.

It is denoted by symbol $\bold{K}$

$\underline {Example }$

▶A fast moving stone has the capacity of breaking a window pane of striking it and thus it had the kinetic energy.

▶A car in motion etc.

◼$\underline \bold {DERIVATION }$

$\textit{The \: kinetic \: energy \: possessed \: by \: a \: moving \: body \:is \: equal \: to \: the \: amount \: of work \: which \: the \: moving \: body \: can \: do \: before \: coming \: to \:rest}$

Suppose a body a mass m is moving with a velocity v. It is brought to rest by applying a constant opposing force F. Let a be the uniform retardation produced by the force and the body travel a distance S before coming to rest.

Then retarding force F = mass × retardation = ma ... ...(I)

Kinetic energy of the body = word done by retarding force in the displacement S before stopping it.

or

Kinetic energy K = retarding force F ×displacement S.

or

K = F × S......(Ii)

Now to calculate the displacement S, we have

initial velocity (u) = v

final velocity (v) =0

Since a is the retardation, so acceleration = -a.

From the relation

${v}^{2} = {u}^{2} + 2aS$

$0 = {v}^{2} - 2aS$

$\therefore,displacement S =\frac{{v}^{2}}{2a}$

Substituting the values of , F and S from eq. (I) , (II) and (III) we get

kinetic energy K = F × S

= m × a ×$\frac{{v}^{2}}{2a}$

=$\frac{1× m ×{v}^{2}}{2a}$

or,

K = $\frac{1}{2} \times m × {v}^{2}$

Kinetic energy = $\frac{1}{2} \times mass × {velocity }^{2}$

Thus kinetic energy of a body depends on square of its velocity of motion.