Grade 12 Physical Sciences · Mechanics

Calculate momentum and its change

Calculate momentum with p = mv, or its change Δp = m(v_f − v_i), keeping track of direction (a 1000 kg car at 20 m/s has 20 000 kg·m/s).

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2)Change momentum gr 12 | IntroKevinmathscience

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Question 1.4 · November 2025 · Paper 1 · National (DBE) · 2 marks

Various options are provided as possible answers to the following questions. Each question has only ONE correct answer. Choose the answer and write only the letter (A–D) next to the question numbers (1.1 to 1.10) in the ANSWER BOOK, e.g. 1.11 E.

1.4 Objects P and Q, with masses m and 2m respectively, have the same momentum, as shown in the diagram.

The velocity of P is ...(2) Diagram for question 1.4

A equal to the velocity of Q.
B half the velocity of Q.
C twice the velocity of Q.
D four times the velocity of Q.

Work it out on paper first. Then mark yourself with the official memo, one tick at a time.

More past paper questions: calculate momentum and its change

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3. Question 4.3.1 · November 2024 · Paper 1 · National (DBE) · 3 marks
Two trolleys, A and B, of masses of $1, 5$ kg and $2$ kg respectively, are held in a stationary position on a straight, horizontal, frictionless track, with a compressed spring between them. The trolleys are released and the spring takes t seconds to return to its natural length. The spring then falls to the ground.
Trolley A moves to the left, while trolley B moves to the right and then up a frictionless inclined plane, rising to a maximum vertical height of $1, 5$ m, as shown in the diagram below.

Ignore the rotational effects of the wheels.
4.3 For the t seconds that the spring takes to return to its natural length:
4.3.1 Calculate the change in momentum of trolley B(3)
Show the memo (3 ticks)Memo
1. ✓
  Formula (any one) $Δ p = m v_{f} - m v_{i}$ OR $F_{n e t} Δ t = Δ p$
  1 mark · Calculate momentum and its change
2. ✓
  Substitution $Δ p = 2 (5, 42 - 0)$
  1 mark · Calculate momentum and its change
3. ✓
  Answer with direction $Δ p = 10, 84$ kg·m·s $^{- 1}$ right
  1 mark · Calculate momentum and its change
4. Question 4.2.2 · November 2025 · Paper 1 · National (DBE) · 4 marks
Cricketers at an academy conduct an experiment to determine the relationship between the contact time and the final momentum of a ball for a constant average net force.

A cricket ball of mass $150$ g is thrown horizontally with a certain initial velocity and is struck by a bat so that the ball moves in the opposite direction, as shown in the diagram below. The average net force acting on the ball is horizontal.

The experiment is repeated using the same ball. The average net force and the initial velocity of the ball are kept constant. The contact time between the bat and the ball is changed EACH time. The results obtained are shown in the sketch graph below.
4.2 Calculate the:
4.2.2 Magnitude of the initial velocity of the ball(4)
Show the memo (4 ticks)Memo
1. ✓
  METHOD 1: FormulaAny one:
  $F_{n e t} Δ t = Δ p$
  $F_{n e t} Δ t = p_{f} - p_{i}$
  $F_{n e t} Δ t = m v_{f} - m v_{i}$
  1 mark · Use the impulse-momentum theorem
2. ✓
  METHOD 1: Substitution of impulse $(225) (0, 03) = \dots$
  1 mark · Use the impulse-momentum theorem
3. ✓
  METHOD 1: Substitution of momentum $(225) (0, 03) = 4, 5 - (0, 15) v_{i}$
  1 mark · Use the impulse-momentum theorem
4. ✓
  METHOD 1: Answer $v_{i} = - 15$ m·s $^{- 1}$
  $v_{i} = 15$ m·s $^{- 1}$
  1 mark · Use the impulse-momentum theorem

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