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

Option 1)
$1/8 ma^{4}t^{2}$

Option 2)
$8 ma^{4}t^{2}$

Option 3)
$4ma^{4}t^{2}$

Option 4)
$1/4 ma^{4}t^{2}$

Answers (2)

best_answer

As we have learned

Net work done by all the forces give the change in kinetic energy -

$W=\frac{1}{2}mv^{2}-\frac{1}{2}mv{_{0}}^{2}$

$W= k_{f}-k_{i}$

- wherein

$m=mass \: of\: the\: body$

$v_{0}= initial\: velocity$

$v= final\: velocity$

$v=\int_{0}^{s}\frac{ds}{\sqrt{s}}=a\int_{0}^{s}dt$

or

$2 \sqrt s \int_{0}^{s}= at$

$s= \frac{a^{2}t^{2}}{4}$

$\therefore v=\frac{a^{2}t}{2}$

total work done = change in K.E

$=1/2mv^{2}-0 =1/2m\left ( \frac{a^{2}t}{2} \right )^{2}$

$w= (1/8) ma^{4}t^{2}$

Option 1)

$1/8 ma^{4}t^{2}$

This is correct

Option 2)

$8 ma^{4}t^{2}$

This is incorrect

Option 3)

$4ma^{4}t^{2}$

This is incorrect

Option 4)

$1/4 ma^{4}t^{2}$

This is incorrect

Posted by

Aadil

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