Question

derive the equation k kinitic energy​

Answer 1

$\bold{\underline{QUESTION}}$

Derive the equation for Kinetic Energy.

$\bold{\underline{ANSWER}}$

Consider the body moving of mass "m" kg moving with velocity 'v' ${ms}^{-1}$ then the work done to stop the body equals to kinetic energy of the body.

$\bold{\boxed{W = F.s}}$

$\mapsto$ W = mas -------------(1)

[since, F = ma]

By third equation of motion,

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

Since, the body is initially at rest, so u = 0

${v}^{2} = 2as \\ as = \frac{1}{2} {v}^{2}$

Substituting the above value in equation (1)

$w = m \times \frac{1}{2} {v}^{2} \\ w = \frac{1}{2} \times m {v}^{2}$

Since, work done is equal to kinetic energy

$k = \frac{1}{2} m {v}^{2}$

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