The figure represents the momentum time (p-t) curve for a particle moving along an axis under the influence of the force. Identify the regions on the graph where the magnitude of the force is maximum and minimum respectively?
If (t₃-t₂) < t₁

Solution

Physics sir · 3 steps

On a p–t graph the slope is the force, so look for the steepest and the flattest line.

1. Slope is force. Newton's second law in momentum form says force is the rate of change of momentum. On a p–t graph, that rate is the slope of the line.

   F = dp/dt = slope of the p–t graph

   Region	Change in p	Time taken	Steepness, so |F|
   a	moderate rise	t₁	moderate
   b	small rise	t₂ - t₁, very long	least steep, minimum
   c	falls all the way to zero, the largest change	t₃ - t₂, shorter than t₁	steepest, maximum

2. Why c beats a. In c the momentum drops from its highest value to zero, a bigger change than the rise in a. The given condition (t₃ - t₂) < t₁ says this bigger change also happens in less time, so the slope of c is larger in magnitude than that of a.
3. So. The force is maximum in magnitude in region c and minimum in region b, which is option (d). The slope in c is negative, but the question asks only for the magnitude.

The idea to keep. Whenever you see a p–t graph, read force as its slope. Compare steepness only. A falling line means the force is negative, but its magnitude can still be the largest.

Answer from the NTA final answer key. Solution by PrepWiser.