Question 144: Work, Energy and Power & Circular Motion

Question

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

Accepted Answer

Given,
$$\upsilon $$ = a $$\sqrt s $$
$$ \Rightarrow $$$$\,\,\,$$ $${{ds} \over {dt}} = a\sqrt s $$
$$ \Rightarrow $$$$\,\,\,$$ $$\int\limits_0^t {{{ds} \over {\sqrt s }}}  = \int\limits_0^z {a\,dt} $$
$$ \Rightarrow $$$$\,\,\,$$ 2$$\sqrt s $$ = at
$$ \Rightarrow $$$$\,\,\,$$ s = $${{{a^2}{t^2}} \over 4}$$
= $${1 \over 2}.{{{a^2}} \over 2}.{t^2}$$
$$	herefore\,\,\,\,$$ acceleration = $${{{a^2}} \over 2}$$
$$	herefore\,\,\,$$ Force (F) = m $$ 	imes $$ $${{{a^2}} \over 2}$$
$$	herefore\,\,\,\,$$ Work done = F. S
= $${{m{a^2}} \over 2} 	imes {{{a^2}{t^2}} \over 4}$$
= $${{m{a^4}{t^2}} \over 8}$$

Answer

$${1 \over 8}\,$$ m a4 t2

Answer

8 m a4 t2

Answer

4 m a4 t2

Answer

$${1 \over 4}\,$$ m a4 t2

Work, Energy and Power & Circular Motion

A body of mass m starts moving from rest along x-axis so that its velocity varies as $\upsilon = 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 the body in the first t seconds after the start of the motion is :

Choose the correct answer: