The position-time $(x-t)$ graph of a moving body of mass $2 \mathrm{~kg}$ is shown in the figure. The…
The position-time $(x-t)$ graph of a moving body of mass $2 \mathrm{~kg}$ is shown in the figure. The impulse on the body at $t=4 \mathrm{~s}$ is
$1.5 \mathrm{~kg}-\mathrm{ms}^{-1}$
$-1.5 \mathrm{~kg}-\mathrm{ms}^{-1}$
$1 \mathrm{~kg}-\mathrm{ms}^{-1}$
$2 \mathrm{~kg}-\mathrm{ms}^{-1}$
Solution
Here, mass of the body, $m=2 \mathrm{~kg}$ and time,
$
t=4 \mathrm{~s}
$
Impulse $=p_f-p_i$
where, $p_i=$ initial momentum,
$p_f=$ final momentum
Impulse $\quad=m v_f-m v_i=m\left(v_f-v_i\right) \quad(\because p=m v)$
As from the graph,
$
v_f=\frac{3-3}{8-4}=0 \text { and } v_i=\frac{3-0}{4-0}=\frac{3}{4}
$
$
\text { Impulse }=2 \times\left(0-\frac{3}{4}\right)=-1.5 \mathrm{~kg}-\mathrm{ms}^{-1}
$
Hence, the correct option is (b)
