Physics • Year 11 • Module 2: Dynamics • Lesson 11

Momentum and Impulse

Lock in the core vocabulary, the two key formulas, sign convention, and the impulse-momentum theorem before tackling harder problems.

Build · Vocab & Recall

1. Term–definition match

The definitions below are shuffled. In the right-hand column write the matching term from this list: momentum, impulse, impulse-momentum theorem, contact time, vector quantity, sign convention, change in momentum, average force, newton second, crumple zone. 10 marks (1 each)

#	Definition	Matching term
1.1	The product of an object’s mass and its velocity; measured in kg m/s.
1.2	The product of average net force and the time interval over which it acts; equal to the change in momentum.
1.3	The physical principle stating that the net impulse acting on an object equals its change in momentum: J = Δp.
1.4	The duration for which two objects remain in contact during a collision.
1.5	A quantity that has both magnitude and direction; momentum and impulse are both this type.
1.6	The rule that assigns positive or negative signs to velocities and momenta based on the chosen positive direction.
1.7	The quantity p_f − p_i = mv_f − mv_i; equals the impulse delivered.
1.8	The force calculated by dividing the impulse by the contact time; written F = Δp/Δt.
1.9	The SI unit of impulse, equivalent to kg m/s; abbreviated N s.
1.10	A region of a vehicle designed to deform during a crash, thereby extending the stopping time and reducing the average force on occupants.

Stuck? Revisit the Formula Reference panel and the Impulse-Momentum Theorem card in the lesson.

2. True or false — with correction

Circle T or F. If the statement is false, write the corrected version on the line below it. 12 marks (1 T/F + 1 correction each)

2.1 Momentum depends only on the speed of an object, not its direction. T / F

2.2 The unit of impulse (N s) is equivalent to the unit of momentum (kg m/s). T / F

2.3 When a ball bounces off a wall and returns at the same speed, its change in momentum is zero because the speed did not change. T / F

2.4 If the same impulse is delivered over a longer contact time, the average force is smaller. T / F

2.5 Crumple zones in cars reduce the change in momentum experienced by occupants during a collision. T / F

2.6 The area under a force-time graph equals the impulse delivered by the force. T / F

Stuck? Revisit the Misconceptions box and the Impulse-Momentum Theorem card in the lesson.

3. Fill-in-the-blank paragraph

Use the word bank to complete the passage. Each word is used once. 8 marks (1 per blank)

Word bank:

contact time · direction · force · impulse · mass · momentum · positive · velocity

___________ is the product of ___________ and ___________; because velocity is a vector, momentum also has a ___________. Before solving any momentum problem, define a ___________ direction so that signs can be assigned correctly to all velocities. ___________ is the product of average net ___________ and the ___________; it equals the change in momentum.

Stuck? Revisit the Formula Reference panel and Card 1 (Momentum) in the lesson.

4. Identify the correct formula

For each scenario, write the formula you would use and identify what quantity you are finding. 8 marks (2 each)

4.1 You know the mass and velocity of an object and need to find the quantity of motion it carries.

4.2 You know the average net force acting on a ball and the duration of contact; you need to find how much momentum was transferred.

4.3 A ball starts at rest and ends up moving at 12 m/s; you need to find how much its momentum changed.

4.4 You know the impulse and the contact time; you need to find the average force during the collision.

Stuck? Revisit the Formula Reference panel in the lesson. Four formulas are shown.

5. Calculate and compare momentum

Complete the table. Define east as positive. Show your working in the space provided. 10 marks (1 per row)

Object	Mass (kg)	Velocity (m/s)	Direction
Cyclist	80	6	East
Cricket ball	0.16	40	West
Car	1200	25	East
Tennis ball	0.058	60	East
Supertanker	4.0 × 10⁸	3	West
Bullet	0.009	900	East
Sprinter	75	10	East
Rugby ball	0.44	14	West
Skateboard + rider	65	4	East
Truck	8000	22	West

Stuck? p = mv. Assign + for east, − for west. State the sign in your answer.

6. Complete the concept map

Draw labelled arrows between the six terms below to show how they connect. Each arrow must carry a linking phrase (e.g. “equals”, “divided by”, “increases when”). Aim for at least 6 labelled arrows. 6 marks (1 per valid labelled arrow)

Supplied terms: impulse · change in momentum · average force · contact time · safety device · injury risk.

impulse

change in momentum

average force

contact time

safety device

injury risk

Try: impulse → equals → change in momentum; impulse → equals → average force × contact time; safety device → increases → contact time; longer contact time → decreases → average force; smaller average force → reduces → injury risk.

Answers — Do not peek before attempting

Q1 — Term–definition match

1.1 momentum • 1.2 impulse • 1.3 impulse-momentum theorem • 1.4 contact time • 1.5 vector quantity • 1.6 sign convention • 1.7 change in momentum • 1.8 average force • 1.9 newton second • 1.10 crumple zone.

Q2 — True / false with correction

2.1 False. Momentum depends on both mass and velocity (p = mv). Because velocity is a vector, momentum also depends on direction, not just speed.

2.2 True. N s = (kg m/s²) × s = kg m/s. The units are equivalent because impulse and change in momentum are the same quantity.

2.3 False. The ball’s velocity reverses direction, so Δp = mv_f − mv_i. If the ball hits at +u and returns at −u, Δp = m(−u − u) = −2mu ≠ 0. Using magnitudes only ignores the direction reversal.

2.4 True. J = FΔt, so F = J/Δt. If J is constant and Δt increases, F decreases.

2.5 False. Crumple zones do NOT reduce the change in momentum; they extend the contact time so that the same Δp is delivered over a longer period, reducing the average force. The Δp (mass × change in velocity) is the same regardless of crumple zones.

2.6 True. Impulse = average force × time = area of the rectangle under the F-t graph. For a varying force, the area under the curve still equals the total impulse.

Q3 — Cloze paragraph

In order: Momentum / mass / velocity / direction / positive / Impulse / force / contact time.

Q4 — Formula identification

4.1 p = mv — finding momentum.

4.2 J = FΔt — finding impulse (which equals Δp).

4.3 Δp = mv_f − mv_i = m(v_f − v_i) — finding change in momentum.

4.4 F = J/Δt = Δp/Δt — finding average force.

Q5 — Momentum table (east = positive)

Cyclist: p = 80 × 6 = +480 kg m/s. Cricket ball: p = 0.16 × (−40) = −6.4 kg m/s. Car: p = 1200 × 25 = +30 000 kg m/s. Tennis ball: p = 0.058 × 60 = +3.48 kg m/s. Supertanker: p = 4.0×10⁸ × (−3) = −1.2×10⁹ kg m/s. Bullet: p = 0.009 × 900 = +8.1 kg m/s. Sprinter: p = 75 × 10 = +750 kg m/s. Rugby ball: p = 0.44 × (−14) = −6.16 kg m/s. Skateboard: p = 65 × 4 = +260 kg m/s. Truck: p = 8000 × (−22) = −176 000 kg m/s.

Q6 — Sample concept map

Correct maps should include arrows such as:

impulse — equals → change in momentum
impulse — equals average force × → contact time
average force — decreases when → contact time increases
safety device — extends → contact time
average force — determines → injury risk
safety device — reduces → injury risk

Award 1 mark per valid labelled arrow (minimum 6, maximum 6 marked).