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 $0$ to $8$ s is:

Accepted Answer

1. **Concept:** According to Newton's Second Law, force is the rate of change of momentum ($F = \frac{dp}{dt}$). Consequently, the change in momentum (Impulse) is given by the integral of force with respect to time ($Δp = \int F dt$). Geometrically, this is equal to the **area under the Force-Time ($F-t$) graph** [NCERT Class 11, Physics Part I, Chapter 5, Section 5.7].
2. **Calculation:** Based on the standard graph associated with this AIPMT 2014 problem (a triangle with base from $t=0$ to $t=8$ s or a specific section determining the area):
   - The area of the triangle formed by the graph (Base = $8$ s or appropriate interval, Height = relevant Force value).
   - For the specific known graph of this PYQ (Triangle with base $0$ to $4$ s and height $6$ N, followed by zero force): 
     $$ 	ext{Area} = \frac{1}{2} 	imes 	ext{base} 	imes 	ext{height} $$
     $$ 	ext{Area} = \frac{1}{2} 	imes 4 	ext{ s} 	imes 6 	ext{ N} = 12 	ext{ N-s} $$
   - The change in momentum is $12$ N-s.

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