Question

A force-time graph for a body (starting from rest) moving along a straight line in $1\text{D}$ is shown in figure. The linear momentum gained by body during time interval $0\text{s}$ to $6\text{s}$ is

• A. $2\text{N.s}$
• B. $4\text{N.s}$
• C. $6\text{N.s}$
• D. Zero

Answer 1

The correct option is B $4\text{N.s}$

$F=\frac{dP}{dt}$
$\Rightarrow \Delta P=\int Fdt$
where $\Delta P=P_f-P_i...\left(i\right)$
$\therefore$Area under the curve of force-time graph gives the change in momentum of the body during that time interval.

$\text{Area under the F-t curve}=2\times 2-2\times 1+2\times 1=4\text{N.s}...\left(ii\right)$
momentum gained between $0$ to $6\text{s}$ is
$\Delta P=P_f-0=P_f$
from eq $\left(i\right)$ and $\left(ii\right)$
$\Rightarrow P_f=4\text{N.s}$