Question

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Derive expression for kinetic energy !!!!!!!

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Answer 1

Answer

Expression of kinetic energy.

Let a body of mass m be kept on a smooth surface having initial velocity u = 0 (rest)

Let a force f is applied on the body due to which body covers a displacement s.

⚝ Work done , W = f.s -------(1)

Since the force f causes motion in the body so body achieves a final velocity v due to acceleration a. So According to Newton's 2nd law of motion.

⚝ f = m.a --------(2)

Putting the value of (2) into (1).

⚝ W = m.a.s -------(3)

By using 3rd equation of motion.

$\implies \rm v^2 = u^2 + 2as$

$\implies \rm v^2 = 0 + 2.a.s$

$\implies \rm v^2 = 2as$

$\implies \rm \frac { v^2 } { 2a } =$ ------- (4)

Putting the value of (4) into (3)

⚝ W = m.a.$\rm \frac { v^2 } { 2a }$

⚝ W = $\rm \frac { 1 } { 2 } mv^2$ -------(5)

$\because$ The capacity of doing work is called energy.

$\therefore$ Work done = Energy( K.E )

So,

$\boxed{\rm K.E=\frac { 1 } { 2 } mv^2}$