Key Idea: Kinematics is the maths of motion — how things move, without asking what causes it. It is the foundation of the whole course, and it is tested in every paper:
Paper 1A
- Multiple choice.
- Quick one-step reads — spot the shape, take a slope or an area.
Paper 1B
- Data and practical work.
- Graph-plotting — plot the points, draw the line, take the gradient.
Paper 2
- Long-answer questions.
- Full determine / show that / sketch — working and units matter.
📈 Reading a motion graph
Almost every kinematics graph question comes down to two readings: take the slope or take the area. Which one depends on which graph you are looking at.
| Graph | Slope (gradient) gives… | Area under the line gives… |
|---|---|---|
| Displacement–time (s–t) | velocity | — (no useful meaning) |
| Velocity–time (v–t) | acceleration | displacement |
| Acceleration–time (a–t) | — (rate of change of a) | change in velocity, Δv |
On a v–t graph the slope is the acceleration and the area is the displacement — mixing these up is the most common motion-graph mistake. Area below the time axis is negative — the object is moving the other way.
🧮 The key equations
For constant acceleration (a straight v–t line) the four suvat equations link the five quantities s, u, v, a and t. All four are given in the data booklet.
- displacement (m)
- initial velocity (m s⁻¹)
- final velocity (m s⁻¹)
- acceleration (m s⁻²)
- time (s)
- displacement (m)
- initial velocity (m s⁻¹)
- final velocity (m s⁻¹)
- time (s)
List your knowns, mark the one you want, and pick the equation that is missing the quantity you neither know nor need. Always write the formula first, then substitute.
🪂 Free fall & projectiles
Free fall is just constant-acceleration motion with a = g = 9.81 m s⁻² pointing down (independent of mass). A projectile splits into two independent motions — constant horizontal velocity, free-fall vertical — sharing one clock.
- horizontal range (m)
- horizontal velocity — stays constant (m s⁻¹)
- time of flight, set by the vertical drop (s)
| Horizontal | Vertical | |
|---|---|---|
| Acceleration | 0 (no sideways force) | g = 9.81 m s⁻² down |
| Velocity | constant (uₓ) | changes by g each second |
| Equation to use | R = uₓ t | the suvat equations with a = g |
💨 Fluid resistance & terminal velocity
Real falling objects meet drag (fluid resistance), which acts against the motion and grows with speed. The suvat equations no longer apply (the acceleration is changing), so this part is described, not calculated.
| Stage of the fall | Drag vs weight | Resultant force | Acceleration |
|---|---|---|---|
| Just released (slow) | drag ≈ 0, weight wins | large, downward | ≈ g (nearly free fall) |
| Speeding up | drag growing, < weight | shrinking | falling below g |
| Terminal velocity | drag = weight | zero | zero — speed now constant |
At terminal velocity the forces are not absent — weight and drag are equal and opposite, so they cancel. Zero resultant force means zero acceleration, so the velocity stays constant.
✍️ Worked examples
A motorbike accelerates uniformly from 6.0 m s⁻¹ to 30 m s⁻¹ over a distance of 90 m. Find its acceleration.
🔒 Model answer plan
See the mark-by-mark plan — for / against / judgement, with marking guidance — in study mode.
🔒 Animated graph
Watch the graph build step by step in study mode.
A tram's velocity–time graph is a straight line rising from 5.0 m s⁻¹ to 17 m s⁻¹ over 8.0 s. Find the distance it travels.
🔒 Model answer plan
See the mark-by-mark plan — for / against / judgement, with marking guidance — in study mode.
A stone is dropped from rest down a well and takes 1.8 s to reach the water. Find (a) its speed on impact and (b) the depth of the well. Take g = 9.81 m s⁻².
🔒 Model answer plan
See the mark-by-mark plan — for / against / judgement, with marking guidance — in study mode.
A ball is thrown horizontally at 7.0 m s⁻¹ from the top of a 31 m cliff. Find (a) the time to land and (b) how far from the base it lands. Take g = 9.8 m s⁻².
🔒 Model answer plan
See the mark-by-mark plan — for / against / judgement, with marking guidance — in study mode.
✅ Quick self-check
Tap each card to check yourself.
What does the slope of a velocity–time graph give? The acceleration. (The area under it gives the displacement.)
You know u, v and a, and you want s. Which suvat equation? The one with no t: v² = u² + 2as.
A ball is thrown straight up. At the very top, what are its velocity and acceleration? Velocity = 0 for an instant; acceleration is still 9.81 m s⁻² downward.
Two balls leave a table at the same height — one dropped, one thrown sideways. Which lands first? Together — vertical motion is independent of the horizontal, so the fall time is the same.
What is the condition for terminal velocity? Drag = weight, so the resultant force is zero and the acceleration is zero — the speed stays constant.
On a v–t graph, what does area below the time axis mean? Negative displacement — the object is moving backwards. Subtract it for the net displacement.
Exam tips
- v–t graph: slope = acceleration, area = displacement. Never swap the two.
- The suvat equations apply only when the acceleration is constant (a straight v–t line) — not once drag matters.
- Choose a suvat equation by the quantity that is missing: list knowns, mark the unknown, pick the equation without the spare one.
- Always write the equation first, then substitute, and keep the unit on every line of working.
- Free fall: a = g = 9.81 m s⁻² down, same for every mass. Decide which direction is positive before you start.
- Projectiles: treat horizontal (constant uₓ) and vertical (free fall) separately — they share only the time.
- Watch the sign: a falling v–t line / a 'deceleration' / area below the axis are all negative.