Question

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

Answer 1

Given,

Mass of the body m=2 kg

Forces acting on the body during the time interval $t=2s$ to $t=4s$.
$S=t^2+2t$
$v=\frac{ds}{dt}=2t+2$
From work energy theorem
$W_{net}=\Delta K.E.=K_f-K_i$
$\frac{1}{2}m(v_f^2-v_i^2)$
$\frac{1}{2}\times 2\left[\right(2\times 4+2{)}^2-(2\times 2+2{)}^2]$
$=64J$
Final answer: $64$