Question

A particle of mass 2 kg is under a force, which causes a displacement in it given by S=(t2 + 2)m.The work done by the force in first 2 s will be
(1) 22J
(2) 56 J
(3) 16 J
(4) 24 J
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Answer 1

Answer:

(3)W= 16 J

Explanation:

Given that

$S=t^2+2$

mass m=2 kg

We know that

Acceleration  $a=\dfrac{dS}{dt}$

$S=t^2+2$

$\dfrac{d^2S}{dt^2}=2$

So $a = 2 \frac{m}{s^2}$

So force on particle F=m x a

F=2 x 2 N

F=4 N

We know that

Work W = ∫F .dS

Now by putting values

W = ∫F .dS

    = ∫4 .dS

W= ∫4.2 t dt

Given that the values t of 0 to 2 sec

So $W=\int_{0}^{2}8 t dt$

So by solving above integral

W= 16 J

So the option 3 is right .