The displacement of a body of mass 2 kg varies with time 't' as S= $t^{2}$ + $2 t$ where S is in metre and 't' is in seconds. the work done by all the forces acting on the body during the time interval t = 2s to 4s is

Zero

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64 J

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4 J

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36 J

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Solution

The correct option is C $64 J$
Given,

$s = t^{2} + 2 t$

$v = \frac{d s}{d t} = \frac{d}{d t} (t^{2} + 2 t) = 2 t + 2$

$K_{f} = \frac{1}{2} m v_{f}^{2} = \frac{1}{2} \times 2 \times (2 \times 4 + 2)^{2} = 100 J$

$K_{i} = \frac{1}{2} m v_{i}^{2} = \frac{1}{2} \times 2 \times (2 \times 2 + 2)^{2} = 36 J$

$W = K_{f} - K_{i} = 100 - 36 = 64 J$

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The displacement of a body of mass 2 kg varies with time 't' as S=t2+2t where S is in metre and 't' is in seconds. the work done by all the forces acting on the body during the time interval t = 2s to 4s is

The correct option is C 64JGiven,s=t2+2tv=dsdt=ddt(t2+2t)=2t+2Kf=12mv2f=12×2×(2×4+2)2=100JKi=12mv2i=12×2×(2×2+2)2=36JW=Kf−Ki=100−36=64J

The displacement of a body of mass 2 kg varies with time 't' as S= $t^{2}$ + $2 t$ where S is in metre and 't' is in seconds. the work done by all the forces acting on the body during the time interval t = 2s to 4s is