Name: Rate of Doing Work
Uploaded: 2019-07-19
Duration: 4 min 44 s
Description: Have you noticed that the electric meter in your house counts your electricity usage in kilowatt-hour? What is a kilowatt-hour? Is it related to a Joule, the...

Question

Derive the formula of kinetic energy.

Accepted Answer

Let an object of mass $m$ , moves with uniform velocity $u$ .
Let us displace it by $s$ , due to a constant force $F$ , acting on it.
Work done on the object of mass $m$ is $W = F \times s$ -------(i)

Due to the force, the velocity changes to $v$ and the acceleration produced is $a$ .
Relationship between $v, u, a$ and $s$ can be given by formula
$v^{2} - u^{2} = 2 a s$
$s = \frac{v^{2} - u^{2}}{2 a}$ -------(ii)
and $F = m a$ -------(iii)

Substitute (ii) and (iii) in (i), we get
$W = F \times s$
$= m a \times \frac{v^{2} - u^{2}}{2 a}$
$W = \frac{1}{2} m (v^{2} - u^{2})$
$u = 0$ , (If object starts from rest)
$W = \frac{1}{2} m v^{2}$
Work done $=$ Change in kinetic energy
$E_{k} = \frac{1}{2} m v^{2}$

Hence, the required equation is obtained.

Derive the formula of kinetic energy.

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