Question

derive an expression for the kinetic energy possesd by an object under motion
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Answer 1

$\huge\mathcal{\underline{\color{purple}Answer}}$

Consider a body of mass "m" moving with an initial velocity "u".

A constant force "F" acts on it and the velocity changes to "v".

Let "s" be the distance covered and "a" be the constant acceleration

We know that ,

v² - u² = 2as

⇒ $S=\frac{V^2-U^2}{2a}$

We know that ,

Work done = Force(F) × displacement (s)

⇒  F = ma

⇒  $W=ma$×$\frac{V^2-U^2}{2a}$

["a" gets cancelled ]

⇒ $W=m$×$\frac{V^2-U^2}{2}$

        $=\frac{1}{2}[V^2-U^2]$

When , initial velocity , u = 0

⇒ $W=\frac{1}{2}mV^2$

☆ K.E = Work done

☆ K.E = $\frac{1}{2}mV^2$

Hope it Helps !!!