Kinematics for 9702: Graphs, SUVAT and Projectiles

Kinematics is topic 2 of the Cambridge AS & A Level Physics 9702 syllabus, and it describes motion without asking what causes it. It is one of the first topics students meet at AS Level, and it underpins dynamics, circular motion, oscillations and the motion of charged particles in fields. If kinematics is secure, a great deal of the course becomes easier.

Where it sits (2025–2027 syllabus)

• Topic 2 (2.1 Equations of motion), AS Level content.
• Examined in Paper 1 (multiple choice) and Paper 2 (AS structured questions). Paper 4 assumes AS knowledge, and kinematic measurements appear in practical work.

What the syllabus requires

You should be able to: 1. define and use distance, displacement, speed, velocity and acceleration; 2. represent motion graphically; 3. find displacement from the area under a velocity–time graph; 4. find velocity from the gradient of a displacement–time graph; 5. find acceleration from the gradient of a velocity–time graph; 6. derive the equations of uniformly accelerated motion from the definitions; 7. solve problems with these equations, including free fall without air resistance; 8. describe an experiment to determine the acceleration of free fall; 9. describe and explain motion with uniform velocity in one direction and uniform acceleration in a perpendicular direction (projectiles).

The key definitions

• Displacement: distance in a specified direction.
• Velocity: rate of change of displacement.
• Acceleration: rate of change of velocity.

Speed and distance are scalars; displacement, velocity and acceleration are vectors. Many errors come from losing track of direction.

Motion graphs

For a curved graph, find the instantaneous gradient by drawing a tangent.

The equations of motion

For uniform acceleration in a straight line: - v = u + at - s = ½(u + v)t - s = ut + ½at² - v² = u² + 2as

Only s = ut + ½at² and v² = u² + 2as are printed in the 9702 data and formulae. Learn the others, and be ready to derive them, as the syllabus requires.

Method: list the five quantities (s, u, v, a, t), mark the three you know and the one you want, then choose the equation that links them.

Worked example 1: acceleration and distance (original)

A car accelerates uniformly from 4.0 m s⁻¹ to 20 m s⁻¹ in 8.0 s. Find its acceleration and the distance travelled.

a = (v − u)/t = (20 − 4.0)/8.0 = 2.0 m s⁻² s = ½(u + v)t = ½(4.0 + 20)(8.0) = 96 m

You can check the distance as the area under the v–t graph: a trapezium with parallel sides 4.0 and 20 and width 8.0.

Worked example 2: vertical motion (original)

A ball is thrown vertically upwards at 15 m s⁻¹. Air resistance is negligible. Find the maximum height and the time taken to reach it. (g = 9.81 m s⁻²)

Take upwards as positive, so a = −9.81 m s⁻². At the top, v = 0. v² = u² + 2as → 0 = 15² − 2(9.81)s → s = 11.5 m v = u + at → 0 = 15 − 9.81t → t = 1.53 s

Sign discipline: choose a positive direction at the start and keep it. Most errors in vertical motion are sign errors.

Worked example 3: a projectile at an angle (original)

A ball is kicked from level ground at 20 m s⁻¹ at 30° above the horizontal. Air resistance is negligible. Find the time of flight, the range and the maximum height.

Resolve: uₓ = 20 cos 30° = 17.3 m s⁻¹; uᵧ = 20 sin 30° = 10.0 m s⁻¹.

• Time of flight: vertical displacement is zero on landing: 0 = 10.0t − ½(9.81)t² → t = 2 × 10.0/9.81 = 2.04 s
• Range: horizontal velocity is constant: 17.3 × 2.04 = 35.3 m
• Maximum height: 0 = 10.0² − 2(9.81)h → h = 5.10 m

The horizontal and vertical motions are independent, linked only by time. This is the whole idea behind syllabus point 9.

Worked example 4: reading a velocity–time graph (original)

A cyclist starts from rest and accelerates uniformly to 12 m s⁻¹ in 4.0 s, travels at constant velocity for 6.0 s, then decelerates uniformly to rest in 3.0 s. Find the deceleration, the total distance and the average speed.

• Deceleration: 12/3.0 = 4.0 m s⁻²
• Distance = area under the graph = ½(4.0)(12) + (6.0)(12) + ½(3.0)(12) = 24 + 72 + 18 = 114 m
• Average speed = total distance / total time = 114/13 = 8.8 m s⁻¹

Note that the average speed is not the mean of the speeds at each stage. It is always total distance divided by total time.

Sketching graphs for a bouncing ball

Questions often ask you to sketch displacement–time, velocity–time or acceleration–time graphs for a ball dropped onto the floor that bounces back up. Taking upwards as positive and ignoring air resistance: - the velocity–time graph is a series of parallel straight lines with gradient −g, with a sudden jump from negative to positive velocity at each bounce; - the acceleration is constant at −g except during the brief contact with the floor; - if energy is lost at each bounce, the rebound speed and maximum height decrease each time.

These sketches test whether you understand vectors and signs, not just the equations.

Measuring g

A common method uses an object falling through a measured height, with the time recorded by light gates or an electronic timer. Plotting a suitable graph (for example, s against t² for an object released from rest) gives a straight line with gradient ½g. Expect to discuss sources of uncertainty, such as the release mechanism and reaction time if timing by hand.

Mistakes that cost marks

1. Confusing distance with displacement, or speed with velocity.
2. Using the equations of motion when acceleration is not uniform.
3. Sign errors in vertical motion.
4. Applying g to the horizontal component of a projectile.
5. Reading a gradient from a graph using points too close together.
6. Giving answers without units or to too many significant figures.

How to practise

• Generate a 9702 kinematics topical PDF from Kambridge Topicals.
• Learn the definitions word for word with Every 9702 Definition You Must Know.
• Sit Paper 1 and Paper 2 past papers from the 9702 past papers library.

Practise by topic

Topical PDFs of 9702 past-paper questions, with mark schemes: Kinematics topical questions · Motion in a circle · Gravitational fields.

Frequently asked questions

Which kinematics equations are given in the exam? Only s = ut + ½at² and v² = u² + 2as appear in the data and formulae.

Do I need to derive the equations? Yes. The syllabus asks you to derive them from the definitions of velocity and acceleration.

Is air resistance included in projectile questions? Calculations assume it is negligible, but you may be asked to describe its effect qualitatively.

Get the foundations right

Engr. Muhammad Waseem, BS Mechanical Engineering (UET Lahore), has taught physics since 2017. He builds kinematics from physical intuition first, so the equations describe ideas you already understand.

Sources: Cambridge International AS & A Level Physics 9702 syllabus for examination in 2025–2027: topic 2.1, the assessment overview and the data and formulae.

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