Question

A body of mass m starts moving from rest along x-axis so that its velocity varies as v = a, where 'a' is a constant and s is the distance covered by the body. The total work done by all the forces acting on the body in the first seconds after the start of the motion is:

Answer 1

V = a not possible when it start from rest it should be a function of t please complete the question

Answer 2

Explanation:

It is given that, a body of mass m starts moving from rest along x-axis so that its velocity varies as :

$v=a\sqrt s$

Here,

a is a constant

s is the distance covered by the body

Acceleration of the body is given by :

$a'=\dfrac{dv}{dt}\\\\a'=\dfrac{a}{2\sqrt s}\dfrac{ds}{dt}\\\\a'=\dfrac{a^2}{2}$

Displacement,

$s'=\dfrac{1}{2}a't^2\\\\s'=\dfrac{1}{2}\times \dfrac{a^2}{2}\times t^2$

Work done is given by :

$W=F'\times s'$

F' = ma'

$W=ma'\times s'\\\\W=m\times \dfrac{a^2}{2}\times \dfrac{a^2t^2}{4}\\\\W=\dfrac{1}{8}ma^4t^2$

Hence, this is the required solution.