A particle moves along the x axis. Its momentum is graphed below as a function of time. Rank the numbered regions according to the magnitude of the force acting on the particle, least to greatest.
A) 1, 2, 3, 4
B) 2, 3, 4, 1
C) 1, 4, 3, 2
D) 1, 3, 4, 2
E) 2, 4, 3, 1

Question

A particle moves along the x axis. Its momentum is graphed below as a function of time. Rank the numbered regions according to the magnitude of the force acting on the particle, least to greatest. 
A) 1, 2, 3, 4 
B) 2, 3, 4, 1 
C) 1, 4, 3, 2 
D) 1, 3, 4, 2 
E) 2, 4, 3, 1

Quizplus · Accepted Answer

The force acting on a particle is equal to the rate of change of its momentum, or F = dp/dt. In region 1, the momentum is constant, so the force acting on the particle is zero. In regions 2, 3, and 4, the momentum is changing, so there is a non-zero force acting on the particle. The magnitude of the force is proportional to the slope of the momentum graph. Thus, the force is smallest in region 2, where the slope is smallest, and largest in region 1, where the slope is largest. Therefore, the regions should be ranked 2, 3, 4, 1, or choice B.

A Particle Moves Along the X Axis