(c) net force = rate of change of momentum; F = Δp/Δt

The idea

Newton's second law states that the net (resultant) force on a body equals the rate of change of its momentum: F = Δp/Δt, where Δp is the change in momentum and Δt is the time interval over which it occurs. For constant mass, Δp = mΔv, so F = mΔv/Δt = ma. The force and the change in momentum are in the same direction.

For example: A 0.15 kg ball changing velocity from 4.0 m s⁻¹ to −4.0 m s⁻¹ in 0.20 s experiences Δp = 0.15 × (−8.0) = −1.2 kg m s⁻¹, giving F = −1.2 / 0.20 = −6.0 N, i.e. 6.0 N opposite to the initial direction.

What earns the marks

• Net force equals the rate of change of momentum: F = Δp/Δt.
• Δp is the change in momentum, calculated as final momentum minus initial momentum.
• For constant mass, F = Δp/Δt reduces to F = ma.
• The direction of the net force is the same as the direction of the change in momentum.
• The time interval Δt must be the duration over which the momentum change occurs.

Common mistakes and how to put them right

• Using initial momentum instead of the change in momentum.

  Put it right: Calculate Δp = p_final − p_initial.

• Ignoring direction when momentum reverses.

  Put it right: Treat reversal as a larger change, e.g. from +4.0 to −4.0 gives Δv = −8.0 m s⁻¹.

• Confusing F = Δp/Δt with F = p/t.

  Put it right: Divide the change in momentum by the time interval, not the momentum itself.

Exam tips

• Write down p_initial and p_final separately before finding Δp.
• Keep signs consistent with your chosen positive direction throughout.
• Check that your answer's direction matches the direction of Δp.