Question

The displacement of an object of mass $3kg$ 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 $2s$ is $\frac{p}{q}joule$ , where $p$ and $q$ are smallest integer values, then what is the value of $p+q$ ?

Answer 1

Answer: 11

$S=\frac{t^2}{3}$
$v=\frac{dS}{dt}$
$\frac{dS}{dt}=\frac{2}{3}t=v;$

$W=\Delta K=K_{t=2}-K_{t=0}$
$W=\frac{1}{2}m\left(v_{t=2}^2-v_{t=0}^2\right)=\frac{1}{2}\cdot 3\left(\frac{16}{9}-0\right)=8/3J$
$\Rightarrow p+q=11$