The displacement of a body of mass 2 kg varies with t as $S = t^{2} + 2 t$ , where S is in meters and t is in seconds. The work done by all the forces on the body during the time interval t = 2s to t = 4s is

36 J

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64 J

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100 J

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120 J

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Solution

The correct option is B 64 J
$S = t^{2} + 2 t$
$V = \frac{d_{3}}{d t} = 2 t + 2$
By work - energy theorem
$△ W_{e x t f o r c e} = △ K$
$△ K = \frac{m}{2} (v f^{2} - v i^{2})$
$= \frac{2}{2} [[2 (4) + 2]^{2} - [2 (2) + 2]^{2}]$
$= 100 - 36 = 64 J$
Option $- B$ is correct

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The displacement of a body of mass 2 kg varies with t as S=t2+2t , where S is in meters and t is in seconds. The work done by all the forces on the body during the time interval t = 2s to t = 4s is

The correct option is B 64 JS=t2+2tV=d3dt=2t+2By work - energy theorem △Wext force=△K△K=m2(vf2−vi2)=22[[2(4)+2]2−[2(2)+2]2]=100−36=64 JOption −B is correct

The displacement of a body of mass 2 kg varies with t as $S = t^{2} + 2 t$ , where S is in meters and t is in seconds. The work done by all the forces on the body during the time interval t = 2s to t = 4s is

The correct option is B 64 J
$S = t^{2} + 2 t$
$V = \frac{d_{3}}{d t} = 2 t + 2$
By work - energy theorem
$△ W_{e x t f o r c e} = △ K$
$△ K = \frac{m}{2} (v f^{2} - v i^{2})$
$= \frac{2}{2} [[2 (4) + 2]^{2} - [2 (2) + 2]^{2}]$
$= 100 - 36 = 64 J$
Option $- B$ is correct