The force $F$ acting on a particle of mass $m$ is indicated by the force-time graph shown below. The change in

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 $8 	ext{ s}$ is:

Accepted Answer

1. **Concept of Impulse:** According to Newton's Second Law of Motion, the rate of change of momentum is equal to the applied force ($F = \frac{dp}{dt}$). Therefore, the change in momentum ($dp$) is given by $F dt$.
2. **Graphical Interpretation:** The change in momentum ($\Delta p$) over a time interval is the integral of force with respect to time: $ \Delta p = \int F dt $. This integral is geometrically equivalent to the **area under the Force-time ($F-t$) graph**.
3. **Calculation:** To determine the change in momentum, one must calculate the area enclosed between the force curve and the time axis from $t=0$ to $t=8 	ext{ s}$.
   - $\Delta p = 	ext{Area under the graph}$.
   - (Note: The specific graph image is not included in the input text. However, for the standard NEET 2014 problem associated with this text, the area calculation of the geometric shapes in the graph yields $12 	ext{ Ns}$).
4. **Conclusion:** The change in momentum is $12 	ext{ Ns}$.

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