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

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

Work, Energy and Power

Solution:

$v=\frac{dS}{dt}=2t + 2$
From work energy theorem;
$W_{\text{net}} =\Delta K.E. =K_{f}-K_{i}$
$=\frac{1}{2}m\left(v^{2}_{f}-v^{2}_{i}\right)$
$=\frac{1}{2} \times 2\left[\left(2 \times 4 +2\right)^{2}-\left(2 \times 2+2\right)^{2}\right]= 64\, J$