Mechanics

Practice

Recall it first, then use it — testing yourself builds the memory, where rereading the notes above only feels easier.

Recall and application shuffled together — you have to work out what each item wants before you can answer it, which is the part the exam actually tests. Both kinds feed the same spacing schedule, so anything you miss comes back sooner.

Say the answer out loud before flipping — that attempt is where the learning happens, even when you get it wrong.

Exam-style only. Instant feedback, shuffled each attempt, best score saved on this device.

What actually comes up

Three questions every year, roughly: a collision/circular-motion question, a forces/equilibrium question (springs, torque, or a slope), and a projectile-motion question — but the exact mix and order moves year to year, always dressed in a real-world scenario. A torque/equilibrium calculation about a pivot has appeared in all three years transcribed here, even though it is easy to mistake for a topic outside "F = ma".

Across 3 years

The pattern — what to prepare

The 2025 paper ↗ Marking schedule ↗

Question One — Acceleration

A rugby player accelerates uniformly from rest at 0.680 m s⁻² and runs 22.0 m, then stops by running into a tackle bag that compresses like a spring.

• a = 0.680 m s⁻²
• distance = 22.0 m

• a How long did it take to run the 22.0 m? Achieved
• b Assuming all the player's energy transfers to the tackle bag, state and justify what happens to the compression distance if the player moves at twice the speed. Merit
• c A penalty shot must clear a crossbar 3.00 m high, 45.0 m away; the ball is kicked at 25.0 m s⁻¹ at 34.0° to the ground. By calculation, decide whether the ball clears the crossbar before hitting the ground. Merit
• d A heavier ball is kicked at the same speed and angle. Without calculating, compare the time in the air, the acceleration, the initial vertical/horizontal speeds, and the horizontal distance travelled to the original ball. Excellence

Question Two — Momentum

An 80.0 kg player moves at 4.30 m s⁻¹; later, the 883 kg All Black scrum (0.354 m s⁻¹) collides with and sticks to the 850 kg Argentinian scrum (0.378 m s⁻¹).

• Player: 80.0 kg, 4.30 m s⁻¹
• All Black scrum: 883 kg, 0.354 m s⁻¹
• Argentinian scrum: 850 kg, 0.378 m s⁻¹

• a Calculate the player's momentum and give the correct unit. Achieved
• b Explain why momentum is more useful than kinetic energy for studying collisions. Achieved
• c Calculate the speed and direction of the combined scrums immediately after they collide and stick together. Excellence
• d Explain how thick pads on a goalpost help protect a player who collides with the post. Excellence

Question Three — Energy

A 68.3 kg player runs up stairs (35.0 m long, 14.1 m high) then sprints; later, two players sit on a uniform 621 N, 3.21 m bench, and two more move in a circle at constant speed.

• Player mass: 68.3 kg
• Stairs: 35.0 m long, 14.1 m high
• Sprint: rest to 7.52 m s⁻¹ in 4.35 s
• Bench: 621 N, 3.21 m; players 669 N and 769 N at given distances

• a Calculate the work done by the player running up the stairs once. Achieved
• b Calculate the average power produced during the sprint. Achieved
• c Add labelled arrows showing all forces on the bench, then calculate the support forces at A and B by taking torques about support A. Merit
• d Add an arrow showing the direction of acceleration for a player moving in a circle at constant speed, and explain how this is possible. Excellence

The 2024 paper ↗ Marking schedule ↗

Question One — Momentum and circular motion

A 10 kg dog runs in a circle at 0.87 m s⁻¹ around a table (centripetal force 15 N), then slides off at a tangent, then is cushioned to a stop by Jono over 2.0 s.

• Dog mass: 10 kg, speed: 0.87 m s⁻¹, centripetal force: 15 N
• Stopping time: 2.0 s

• a Add a labelled arrow showing the force on the dog as it runs in a circle at constant speed. Achieved
• b Calculate the radius of the dog's path, then explain its velocity immediately after it slides off at a tangent. Achieved
• c Calculate the force experienced by the dog in the 2.0 s cushioned collision, and use physics principles to explain why Jono cushioned it rather than letting it stop in 0.10 s. Excellence
• d Jono's 10 kg dog runs at 1.1 m s⁻¹ toward the neighbour's 12 kg dog; they collide, stick together, and slide at 0.30 m s⁻¹. Calculate the neighbour's dog's speed before the collision. Merit

Question Two — Springs and equilibrium

0.11 kg of flour is measured on a three-spring kitchen balance, each spring compressing 0.01 m; later, Jono chooses stairs or a ramp, and a spice rack hangs from two wires.

• Flour: 0.11 kg, spring compression: 0.01 m, 3 springs
• Spice rack: ginger 0.030 kg at 0.15 m, salt 0.50 kg at 0.050 m, rack 0.37 kg and 0.40 m long, max wire tension 5.0 N

• a Add labelled arrows showing the two forces acting on the flour with the springs compressed. Achieved
• b Calculate the spring constant for one spring. Merit
• c Compare the stairs and the ramp by work done, force required, and power. Merit
• d State the conditions for the spice rack to be in equilibrium, then decide by calculation whether the wires can hold the ginger and salt. Excellence

Question Three — Motion

An apple is rolled at 0.56 m s⁻¹, stopping after 4.0 s; it is then thrown at 5 m s⁻¹ at 40° toward Jono, 2.0 m away, under a 1.5 m ceiling.

• Roll: 0.56 m s⁻¹ initial, stops in 4.0 s
• Throw: 5 m s⁻¹ at 40°
• Ceiling height: 1.5 m, distance to Jono: 2.0 m

• a Calculate the acceleration of the rolling apple. Achieved
• b Calculate the vertical and horizontal components of the initial throw velocity. Merit
• c Identify the type of motion, add labelled force and velocity arrows at three points on the flight path, and describe how the vertical and horizontal velocities change throughout. Merit
• d By calculating the maximum height and horizontal distance covered, determine whether the apple reaches Tony without hitting the 1.5 m ceiling. Excellence

The 2023 paper ↗ Marking schedule ↗

Question One — Softball match

A player accelerates from home plate to first base, taking 6.61 s to reach 5.45 m s⁻¹; later a 0.180 kg ball thrown at 44.4 m s⁻¹ is caught over 0.510 s, and a 50 kg player collides with and sticks to a 60 kg player.

• t = 6.61 s, v = 5.45 m s⁻¹
• Ball: 0.180 kg, 44.4 m s⁻¹, stops in 0.510 s
• Collision: 50 kg + 60 kg (0.4 m s⁻¹) → 2 m s⁻¹ combined

• a Show that the average acceleration is 0.825 m s⁻². Achieved
• b Calculate the maximum displacement to first base, and explain why this might differ from the actual distance travelled. Merit
• c Define impulse, calculate the average force of the ball on the padded glove, and explain the advantages of catching with a relaxed arm and a padded glove. Merit
• d State what physical quantity is conserved during the collision, then calculate the initial speed of the 50 kg player. Excellence

Question Two — Cornering

A 55.0 kg player moves at a constant 7.00 m s⁻¹ around a 15.0 m radius circular path, then runs onto a slippery, muddy patch.

• Mass: 55.0 kg, speed: 7.00 m s⁻¹, radius: 15.0 m

• a Calculate the centripetal force acting on the player. Achieved
• b Add labelled arrows showing the direction of the force, acceleration, and velocity of the player. Achieved
• c Name the force supplying the centripetal force, and explain how the player can be moving at constant speed yet accelerating. Merit
• d Describe and explain fully, using physics principles, the effect(s) the slippery mud will have on the player's motion. Excellence

Question Three — Projectiles

A ball is hit at 22.0 m s⁻¹ at 35.0°; later, a 110 kg coach and a 74.0 kg substitute sit on a uniform 40.0 kg bench.

• Launch: 22.0 m s⁻¹ at 35.0°
• Bench: 40.0 kg, coach 110 kg, player 74.0 kg, at given distances

• a Show that the vertical component of the initial velocity is 12.6 m s⁻¹. Achieved
• b Calculate the maximum height reached by the ball. Merit
• c Add labelled force arrows at three points on the flight path, then describe and explain how forces, acceleration, and horizontal/vertical velocities change throughout the flight. Merit
• d Add arrows for all forces on the bench, then determine the support forces at A and B by calculating torques about support B. Excellence

Grades above are read from each year's own Achievement/Merit/Excellence evidence statement, condensed to the actual task — the schedules also grade holistically per question on a 0–8 scale, not a fixed mark per bullet.

Past exams & resources

⏱ Timed opens the paper and starts a countdown matching the exam length. Official NZQA PDFs. If a link 404s, that year’s paper may sit under a slightly different code: browse the NZQA subject page.