Kinematics: Practice Questions

These are original questions written for Marlbridge, in the style and at the standard of the examination. They are not reproduced past-paper questions — the IB holds copyright in its own papers. Use these alongside the official past papers available through your school or the IB store, since past papers remain the best guide to the IB’s exact question phrasing, command terms and mark schemes.

Related: Kinematics revision notes

Section A tests core definitions and single-step recall, Section B applies SUVAT to more complex projectile and deceleration scenarios, and Section C tests graphical interpretation alongside a free-fall calculation — together these mirror the range of demand you should expect across a real kinematics exam question, from simple recall through multi-step application to conceptual graph sketching.

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Section A

1. A car accelerates uniformly from rest to 20 m/s in 8 seconds. Calculate its acceleration. [2]

Section A questions test single-step recall and application of a single SUVAT relationship or graph fact — these are the marks that should be secured quickly and confidently before moving on to the more time-consuming multi-step questions in Sections B and C.

2. State the quantity represented by the gradient of a displacement-time graph. [1]

Section B

3. A ball is thrown horizontally from a cliff top with a speed of 12 m/s. It lands 2.4 s later. (g = 9.81 m/s², ignore air resistance)

(a) Calculate the height of the cliff. [3] (b) Calculate the horizontal distance travelled by the ball. [2] (c) Calculate the vertical component of the ball’s velocity as it lands. [2]

4. A cyclist decelerates uniformly from 15 m/s to rest over a distance of 45 m. Calculate the deceleration. [3]

Section C

5. Sketch (in words) the shape of a displacement-time graph for an object that starts at rest and undergoes constant positive acceleration for 5 seconds, then travels at constant velocity for a further 5 seconds. [3]

6. A stone is dropped from rest from a height of 20 m. (g = 9.81 m/s², ignore air resistance) (a) Calculate the time taken to reach the ground. [2] (b) Calculate the velocity with which it strikes the ground. [2]

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Answers

1. a = (v − u) / t = (20 − 0) / 8 = 2.5 m/s² [2].

2. Velocity [1].

3. (a) Vertical motion only: s = ut + ½at² , with u = 0 (no initial vertical velocity) [1]. s = 0 + ½ × 9.81 × 2.4² = ½ × 9.81 × 5.76 = 28.3 m [2]. (b) Horizontal motion is unaffected by gravity: s = v × t = 12 × 2.4 = 28.8 m [2]. (c) v = u + at, with u = 0 (vertically): v = 0 + 9.81 × 2.4 = 23.5 m/s (downward) [2].

4. Using v² = u² + 2as, with v = 0, u = 15, s = 45: 0 = 15² + 2a(45) → 0 = 225 + 90a → a = −225/90 = −2.5 m/s² (i.e. a deceleration of 2.5 m/s²) [3].

5. For the first 5 seconds, the graph is a curve with increasing gradient — starting flat (zero velocity) and steepening throughout, since gradient = velocity and velocity is increasing under constant acceleration [2]. For the next 5 seconds, the graph becomes a straight line with constant (non-zero) gradient, since velocity is now constant [1].

6. (a) s = ut + ½at², with u = 0: 20 = 0 + ½ × 9.81 × t² → t² = 40/9.81 = 4.08 → t = 2.02 s [2]. (b) v = u + at = 0 + 9.81 × 2.02 = 19.8 m/s [2]. (Alternatively, v² = u² + 2as = 0 + 2 × 9.81 × 20 = 392.4 → v = 19.8 m/s.)

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Why free-fall questions are a special case of projectile motion

Question 6 is a vertical-only version of the projectile-motion problems in Question 3 — there is no horizontal component at all, since the stone is dropped rather than thrown. This makes it the simplest possible application of SUVAT: a single direction, a known constant acceleration (g), and an initial velocity of zero. Recognising free fall as a special case — rather than a separate topic requiring different equations — is what lets you transfer confidently between “drop” and “throw horizontally” question types, since both reduce to the same vertical SUVAT working once the horizontal component (zero in one case, constant in the other) is set aside.

Where marks are usually lost

• Mixing horizontal and vertical quantities in projectile-motion calculations instead of solving each direction independently.
• Sign errors — not defining a consistent positive direction before substituting into SUVAT equations.
• Forgetting units, or giving a final answer without stating whether a quantity like velocity has a direction.
• Using the wrong SUVAT equation for the variables given — check which quantity is missing before choosing an equation.
• On graph-description questions like Q5, confusing the shape of a displacement-time graph with a velocity-time graph — a constant acceleration produces a curved displacement-time graph but a straight-line velocity-time graph.
• Rounding intermediate values (like t in Q6) too early, which compounds error into the final answer — keep extra decimal places until the last step.
• Spending too long securing full marks on a Section A question worth 1-2 marks while running short of time for the higher-value Section B and C questions.