# 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: Option 1) 24 Ns Option 2) 20 Ns Option 3) 12 Ns Option 4) 6 Ns

As we learnt in

Impulse -

$\vec{I}=\int_{t_{1}}^{t_{2}}\vec{F}\cdot dt$

$\ast\left [ MLT^{-1} \right ]$

- wherein

Area of F-t graph gives change in momentum

For 0 to 2 sec

$\Delta P_{1}=\frac{1}{2}\times2\times 6=6kg-m/s$

For 2-4

$\Delta P_{2}=2\times(-3)=-6kg-m/s$

$\Delta P_{3}=4\times 3=12kg-m/s$

Total change in momentum 0 to 8 sec

$\Delta P_{net}=\Delta\: P_{1}+\Delta\: P_{2}+\Delta\: P_{3}$

$=6-6+12=12N-s$

Correct option is 3.

Option 1)

24 Ns

Incorrect

Option 2)

20 Ns

Incorrect

Option 3)

12 Ns

Correct

Option 4)

6 Ns

Incorrect

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