The force-time (F – t) curve of a particle executing linear motion is as shown in the figure. The momentum acq

Question

The force-time (F – t) curve of a particle executing linear motion is as shown in the figure. The momentum acquired by the particle in the time interval from zero to 8 seconds will be:

Accepted Answer

1. **Concept:** According to Newton's Second Law, the force is the rate of change of momentum ($F = dp/dt$). The change in momentum (Impulse) over a time interval is the integral of force with respect to time: $\Delta p = \int F dt$ [Source 62, 63].
2. **Graphical Interpretation:** In a Force-time ($F-t$) graph, this integral corresponds to the area under the curve. Area above the time axis represents positive impulse (increase in momentum), and area below represents negative impulse (decrease in momentum).
3. **Calculation:** The momentum acquired is the net area under the curve from $t=0$ to $t=8$ s. For the answer to be 'Zero', the graph must have equal positive and negative areas, resulting in a net impulse of zero [Source 73, 74].

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