Question

Derive the formula for kinetic energy.

Answer 1

$\huge{Kinetic\: Energy}$

The kinetic energy possessed by a moving body is equal to the amount of work done which a moving body can do before coming to rest.

$<b>Proof$

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

F=ma........... (1)

K=F×S.......... (2)

Now to calculate displacement S, we have

initial velocity (u) =v,
final velocity (v) =0

Since a is the retardation, so acceleration= –a

From relation

${v}^{2} = {u}^{2} + 2as \\ 0 = {v}^{2} - 2as$

$s = \frac{ {v}^{2} }{2a} .......(3)$

Substituting the values of F and S from equation (1) and (3) in equation (2) we get

$k = fax \\ k = ma \times \frac{ {v}^{2} }{2a} \\ k = \frac{1}{2} mv {}^{2}$

Answer 2

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

F=ma........... (1)

K=F×S.......... (2)

Now to calculate displacement S, we have

initial velocity (u) =v,

final velocity (v) =0

Since a is the retardation, so acceleration= –a

From relation

Substituting the values of F and S from equation (1) and (3) in equation (2) we get