A 1 kg mass moves along a frictionless horizontal track with an applied force that linearly increases from 0 to 4 N over 2 s. What is the approximate change in momentum after 2 s?

A 1 kg mass moves along a frictionless horizontal track with an applied force that linearly increases from 0 to 4 N over 2 s. What is the approximate change in momentum after 2 s?

• A. 2 kg·m/s
• B. 4 kg·m/s
• C. 8 kg·m/s
• D. 0 kg·m/s

Answer: (B)

Momentum changes because of impulse, which is the integral of force over time. Here the force grows linearly from 0 to 4 N over 2 seconds, so the force-time graph is a triangle with base 2 s and height 4 N. The impulse is the area of that triangle: (1/2) × 2 × 4 = 4 N·s, which equals 4 kg·m/s. That’s the change in momentum. Since the mass is 1 kg, the velocity would increase by ∆v = ∆p / m = 4 m/s, but the essential point is the momentum changes by 4 kg·m/s due to the impulse from the applied force.

Momentum changes because of impulse, which is the integral of force over time. Here the force grows linearly from 0 to 4 N over 2 seconds, so the force-time graph is a triangle with base 2 s and height 4 N. The impulse is the area of that triangle: (1/2) × 2 × 4 = 4 N·s, which equals 4 kg·m/s. That’s the change in momentum. Since the mass is 1 kg, the velocity would increase by ∆v = ∆p / m = 4 m/s, but the essential point is the momentum changes by 4 kg·m/s due to the impulse from the applied force.