Question

prove that work done is equal to change in kinetic energy​

Answer 1

$\large \bold{ \underline{ \underline{ \sf To \: prove : \: \: }}}$

$\to$ Work done = Change in kinetic energy

$\large \bold{ \underline{ \underline{ \sf Proof : \: \: }}}$

$\star$ Force = f

$\star$ Displacement = s

$\star$ Mass = m

$\star$ Acceleration = a

$\star$ Initial velocity = u

$\star$ Final Velocity = v

Now ,

$\sf Work \: done = Force × Displacement \\ \\ \sf</p><p>Work \: done = f × s \\ \\ \sf</p><p>Work \: done = ma × s \\ \\ \sf</p><p>Work \: done = ms \times ( \frac{ {v}^{2} - {u}^{2} }{2s} ) \\ \\ \sf Work \: done = \frac{m}{2} ( {v}^{2} - {u}^{2} ) \\ \\ \sf Work \: done = \frac{1}{2} m {v}^{2} - \frac{1}{2}m {u}^{2}$

$\sf \large { Hence \: proved }$