Q. The displacement of an object of mass $3 \, kg$ is given by the relation $S=\frac{1}{3}t^{2}$ , where $t$ is time in seconds. If the work done by the net force on the object in $2 \, s$ is $\frac{p}{q} \, joule$ , where $p$ and $q$ are smallest integer values, then what is the value of $p+q$ ?
NTA AbhyasNTA Abhyas 2020Work, Energy and Power
Solution:
$S=\frac{t^{2}}{3}$
$v=\frac{d S}{d t}$
$\frac{d S}{d t}=\frac{2}{3}t=v; \, $
$W=\Delta K=K_{t = 2}-K_{t=0}$
$W=\frac{1}{2}m\left(v_{t = 2}^{2} - v_{t = 0}^{2}\right)=\frac{1}{2}\cdot 3\left(\frac{16}{9} - 0\right)= \, 8 / 3 \, J$
$\Rightarrow \, \, p+q=11$
$W=\Delta K=K_{t = 2}-K_{t=0}$
$W=\frac{1}{2}m\left(v_{t = 2}^{2} - v_{t = 0}^{2}\right)=\frac{1}{2}\cdot 3\left(\frac{16}{9} - 0\right)= \, 8 / 3 \, J$
$\Rightarrow \, \, p+q=11$