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Objects in motion review
A summary of the whole Objects in Motion chapter, every formula with its units, key words, and a mixed test covering displacement and vectors, speed, velocity and acceleration, motion graphs, Newton's three laws, momentum, energy and work, and road safety.
Use this page to check the whole chapter. Read the summary, make sure you can use every formula and explain every key word, then do the test without looking back.
Chapter summary
| Topic | What you need to know |
|---|---|
| 5A Distance, displacement and vectors | Scalars have size only; vectors have size and direction (arrows). Distance = total path; displacement = straight-line change in position with direction. A lap: distance 400 m, displacement 0. Pythagoras and tan for size and bearing. Add vectors head to tail. |
| 5B Speed and velocity | Average speed = total distance ÷ total time; km/h ÷ 3.6 = m/s. Instantaneous speed. Velocity = speed with direction; average velocity = displacement ÷ time. Ticker timer: dot every 0.02 s, 5 gaps = 0.1 s; light gates, motion sensors, video. |
| 5C Acceleration | a = (v − u) ÷ t in m/s². Speeding up, slowing down (deceleration) or changing direction. g ≈ 9.8 m/s². From rest, d = ½ a t², so a = 2d ÷ t². Accelerometers; g-forces. |
| 5D Motion graphs | Position–time: gradient = velocity; flat = stationary. Velocity–time: gradient = acceleration; flat = constant velocity; area = displacement. |
| 5E Newton's first law | Net force = vector sum of forces. No net force: at rest or constant velocity. Inertia increases with mass. Friction explains why things slow down. Circular motion needs a centripetal force; without it, motion continues along the tangent. Returning boomerangs use sideways lift as a centripetal force. |
| 5F Newton's second law | F = m a with F the net force. 1 N gives 1 kg an acceleration of 1 m/s². Weight W = m g. Trolley and hanging mass: a ∝ F, a ∝ 1 ÷ m. Terminal velocity when air resistance = weight. |
| 5G Third law and momentum | Equal and opposite forces on different objects (walking, rockets, recoil). p = m v. Total momentum is conserved in collisions and explosions; KE is conserved only in elastic collisions. F × t = change in momentum. |
| 5H Work and energy in motion | KE = ½ m v² (doubling speed → 4 × KE). GPE = m g h. W = F × d. Energy is conserved; falling from rest, v = √(2 g h). Bounce efficiency = rebound height ÷ drop height. Energy chains in sport (Snicko, Hot Spot). The woomera does more work on a spear. |
| 5I Road safety and collisions | Stopping distance = reaction distance (v × t) + braking distance (v² ÷ 2a). F × d = KE and F × t = Δp: longer stops mean smaller forces. Crumple zones, safety cell, seatbelts, airbags, head restraints; ABS, ESC, AEB; ANCAP ratings. Lower speeds greatly reduce pedestrian deaths. |
Formulas
| What | Formula | Units |
|---|---|---|
| Average speed | v = d ÷ t | m/s, m, s (or km/h, km, h) |
| Unit conversion | km/h ÷ 3.6 = m/s | |
| Average velocity | velocity = displacement ÷ time | m/s |
| Acceleration | a = (v − u) ÷ t | m/s², m/s, s |
| Distance from rest at constant a | d = ½ a t² | m, m/s², s |
| Newton's second law | F = m a | N, kg, m/s² |
| Weight | W = m g | N, kg, 9.8 N/kg |
| Momentum | p = m v | kg m/s |
| Impulse | F × t = m v − m u | N s = kg m/s |
| Kinetic energy | KE = ½ m v² | J, kg, m/s |
| Gravitational potential energy | GPE = m g h | J, kg, N/kg, m |
| Work | W = F × d | J, N, m |
| Efficiency | useful energy out ÷ energy in × 100 | % |
| Stopping distance | v × reaction time + v² ÷ (2a) | m |
Putting it together
Every idea in this chapter builds on the one before. To describe motion you need a reference point and vectors: displacement, velocity and acceleration all have directions, and motion graphs show how they change. Newton's laws then explain the changes. With no net force, nothing changes (first law). A net force produces an acceleration that depends on the mass (second law, F = ma). Forces always come in equal and opposite pairs acting on different objects (third law), which is why momentum is conserved when objects collide or push apart. Energy gives a second, powerful way to look at the same events: a net force doing work changes an object's kinetic energy, and energy is never lost, only transformed, often into heat and sound. Road safety brings all of it together: reaction distance comes from velocity, braking distance from kinetic energy and work, and the injuries in a crash from how quickly momentum is removed, which is exactly what seatbelts, airbags and crumple zones are designed to slow down.
Key words
acceleration · action–reaction pair · airbag · average speed · bearing · braking distance · centripetal force · conservation of energy · conservation of momentum · crumple zone · deceleration · displacement · distance · efficiency · elastic collision · elastic potential energy · force · g · gradient · gravitational potential energy · impulse · inertia · instantaneous speed · joule · kinetic energy · mass · momentum · net force · newton · Newton's laws · position–time graph · reaction distance · resultant · scalar · speed · stopping distance · terminal velocity · ticker timer · vector · velocity · velocity–time graph · weight · work
Test yourself
A runner completes 3 laps of a 400 m track in 6 minutes, finishing at the start line. Their average speed and average velocity are
1200 m ÷ 360 s = 3.3 m/s; displacement is zero, so average velocity is zero.
A train starts from rest and reaches 25 m/s in 50 s. Its acceleration is
a = 25 ÷ 50 = 0.5 m/s².
The area under a velocity–time graph gives the
Velocity × time = displacement.
A passenger lurches backwards as a bus pulls away. This is best explained by
The passenger's body tends to stay at rest while the bus accelerates forwards.
A 5 kg box is pushed with 50 N and accelerates at 2 m/s². The friction force is
Net force = 5 × 2 = 10 N, so friction = 50 − 10 = 40 N.
A 3 kg trolley at 4 m/s collides and sticks to a stationary 1 kg trolley. Their common velocity is
Momentum 12 kg m/s ÷ 4 kg = 3 m/s.
A moving car has 10 kJ of kinetic energy. It hits a wall and bounces back with 2000 J of KE, and 1250 J becomes sound and heat. The work done damaging the car and wall is
10 000 − 2000 − 1250 = 6750 J (conservation of energy).
Doubling a car's speed makes its braking distance
Braking distance ∝ v² (because KE ∝ v²).
Label the areas on the velocity–time graph.
Which of Newton's laws best explains each situation?
Order these stopping distances for an alert driver on a dry road, shortest first.
When an object moves at a constant in a straight line, Newton's law says it will continue unless a net force acts. Newton's law says a net force causes an . In a collision, total is conserved. Energy cannot be created or .
A watermelon is dropped from a height of 5 m onto a person's head. Using Newton's laws, momentum and energy, explain in detail what happens, and why a helmet would reduce the injury. (Take the watermelon's mass as 4 kg and ignore air resistance.)
The watermelon starts with GPE = m g h = 4 × 9.8 × 5 = 196 J. As it falls this becomes kinetic energy, so it reaches the head at v = √(2 × 9.8 × 5) = 9.9 m/s, with momentum 4 × 9.9 ≈ 40 kg m/s downwards. By Newton's first law it would keep moving downwards, so a force is needed to stop it. The head provides a large upward force that decelerates the melon over a very short distance (second law: a big force gives a big deceleration). By Newton's third law, the melon pushes down on the head with a force of exactly the same size, which is what injures the person, while the head's force on the melon splits it open. In terms of energy, the melon's 196 J of KE is transformed into work breaking the melon and compressing the person's scalp and skull, plus some heat and sound. A helmet has a hard shell and a crushable foam liner. The foam crushes, increasing the distance and time over which the melon (and the head) are stopped. Since F × d = KE and F × t = change in momentum, the same energy and momentum are removed with a much smaller force, and the shell spreads that force over a larger area, so the injury is far less severe.