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The force $F$ acting on a particle of mass $m$ is indicated by the force-time graph shown below. The change in momentum of the particle over the time interval from zero to $8\, s$ is .......... $N-s$
$24$
$20$
$12$
$6$
Solution
$\begin{array}{l}
Chenge\,in\,momentum\, = Area\,under\,F – graph\\
\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,in\,that\,{\rm{interval}}\\
\,\,\,\,\,\,\, = Area\,of\,\Delta ABC – Area\,of\,{\rm{rectangle}}\,CDEF\\
\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, + Area\,of\,{\rm{rectangle}}\,{\rm{FGHI}}\\
\,\,\,\,\,\,\, = \,\frac{1}{2} \times 2 \times 6 – 3 \times 2 + 4 \times 3 = 12\,N\,s
\end{array}$
