First slide

Second law

Question

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

Moderate

A

24 Ns
B

20 Ns
C

12 Ns
D

6 Ns

Solution

$F = \frac{dp}{dt} \Rightarrow dp = F . dt or \int_{p_{i}}^{p_{f}} dp = \int F . dt$
Change in momentum = Area under the F versus t graph in the interval
= $(\frac{1}{2} \times 2 \times 6) - (2 \times 3) + (4 \times 3)$
= 6-6+12 = 12 NS

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