Question

Write an expression for the kinetic energy of a body of mass m moving with a velocity v.

Answer 1

K. E. = 1/2 mv^2

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 ​​​​​​$\times \frac{v^2-u^2}{2a}$


["a" gets cancelled ]

W = m $\times \frac{v^2-u^2}{2}$​​​​​
= 1/2 m[v² - u² ]


When , initial velocity , u = 0

W = 1/2mv²

K.E = Work done
= 1/2 mv²