Question

please answer the pinned question friends
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Answer 1

Answer:

Hope it helps you.......

Explanation:

Answer 2

Answer:

Given:

Velocity vs Displacement relationship as :

$v = \sqrt{9 + 4s}$

Mass of object = 2 kg

To find:

Work done in time 1 - 2 seconds.

Concept:

As per Work Energy Theorem , we can say that work done by all forces is equal to the change in Kinetic Energy in the specified time interval.

Calculation:

$\therefore \: v = \sqrt{9 + 4s}$

$= > \dfrac{ds}{dt} = \sqrt{9 + 4s}$

$= > \int \dfrac{ds}{ \sqrt{9 + 4s} } = \int \: dt$

$= > \dfrac{ \sqrt{9 + 4s} }{2} = t + c$

Assuming s = 0 , when t = 0 ;

$= > \frac{ \sqrt{9} }{2} = c \\ = > c= \frac{3}{2}$

So our displacement vs time Equation comes as :

$\: \: \: \: \: \: \: \: \: \: \: \: \boxed{ \bold{ \red{ \sqrt{9 + 4s} = 2t + 3}}}$

So at t = 2 seconds , we get :

$\sqrt{9 + 4s} = 7 \\ = > 9 + 4s = 49 \\ = > 4s = 40 \\ = > s = 10 \: m$

Now putting the values in work energy theorem :

Work done = Change in KE

$= > w = \frac{1}{2} m {v_{2}}^{2} - \frac{1}{2} m {v_{1}}^{2}$

$= > w = \frac{1}{2} m \{ {v_{2}}^{2} - {v_{1}}^{2} \}$

$= > w = (\frac{1}{2} \times 2) \small{\{ { \sqrt{(9 + 40)} }^{2} - { \sqrt{9} }^{2} \}}$

$= > w = 40 \: joules$

So final answer :

$\boxed{ \huge{ \blue{option \: d)}}}$