Kinematics
Distance and displacement, speed and velocity, acceleration, displacement–time and velocity–time graphs, and free fall, for G3 Pure and O-Level Physics.
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Before you begin
Kinematics describes how things move, without asking what makes them move. The lessons start with the quantities of motion (distance and displacement, speed and velocity, acceleration), then read and plot displacement–time and velocity–time graphs, and finish with free fall and the ticker tape timer.
Be comfortable with: scalars and vectors, because displacement, velocity and acceleration all have a direction.
Learning goals
- State what speed means
- State what velocity means, including its direction
- Calculate average speed from total distance and total time
- Calculate acceleration as change in velocity divided by time taken
- State what uniform acceleration means
- Interpret examples of non-uniform acceleration
- Plot and interpret displacement–time and velocity–time graphs in one dimension
- Deduce rest and uniform or non-uniform velocity from a displacement–time graph
- Deduce rest, uniform velocity and uniform or non-uniform acceleration from a velocity–time graph
- Use signed area under a velocity–time graph to determine displacement
- Recall constant free-fall acceleration near Earth as approximately 10 m/s²
Syllabus statements covered
- state what is meant by speed and velocity
- calculate average speed = distance travelled / time taken
- state what is meant by uniform acceleration and calculate the value of acceleration using change in velocity / time taken
- interpret given examples of non-uniform acceleration
- plot and interpret a displacement-time graph and a velocity-time graph for motion in one dimension
- deduce from the shape of a displacement-time graph when a body is: (i) at rest (ii) moving with uniform velocity (iii) moving with non-uniform velocity
- deduce from the shape of a velocity-time graph when a body is: (i) at rest (ii) moving with uniform velocity (iii) moving with uniform acceleration (iv) moving with non-uniform acceleration
- calculate the area under a velocity-time graph to determine the displacement for motion with uniform velocity or uniform acceleration
- state that the acceleration of free fall for a body near to the Earth is constant and is approximately 10 m/s²
Lessons
Work through them in order.
Motion quantities
- Distance vs displacementTell total path length from change in position, and give a displacement its direction.
- Speed vs velocityCalculate average speed and average velocity for a journey, and give a velocity its direction.
- AccelerationCalculate acceleration from a change in velocity, and tell uniform from non-uniform acceleration.
Core graph skills
- Reading displacement–time and velocity–time graphsDescribe motion from a graph's shape, and find velocity and acceleration from its gradient.
- Reading curved motion graphsTell direction from speed on a curved graph, and recognise non-uniform acceleration.
- Plotting kinematics graphs from dataPlot motion data on sensible scales, and decide whether to join the points or draw a line of best fit.
- Area under a velocity–time graphFind displacement and distance travelled from the area under a velocity–time graph.
Free fall
Practical context
Beyond the syllabus
Practise and check
Or choose
Topic reference
Quick reference
| Quantity or graph feature | Equation or meaning | Unit |
|---|---|---|
| average speed | total distance travelled ÷ total time taken | m s⁻¹ |
| average velocity | total displacement ÷ total time taken, with direction | m s⁻¹ |
| acceleration | a = (v-u)/t | m s⁻² |
| acceleration of free fall | g ≈ 10 m s⁻², downwards, near the Earth | m s⁻² |
| gradient of a displacement–time graph | velocity | m s⁻¹ |
| gradient of a velocity–time graph | acceleration | m s⁻² |
| area under a velocity–time graph | displacement (area below the time axis counts as negative) | m |
Core knowledge to remember
- Distance is the total length of the path; displacement is the change in position, with a direction.
- Speed is distance travelled per unit time; velocity is displacement per unit time, so it has a direction.
- Uniform acceleration means the velocity changes by equal amounts in equal times. Non-uniform acceleration means it does not.
- An object speeds up when its acceleration points the same way as its velocity, and slows down when they point opposite ways.
- On a displacement–time graph, a horizontal line means at rest and a straight sloping line means uniform velocity.
- On a velocity–time graph, a horizontal line means uniform velocity, a straight sloping line means uniform acceleration and a curve means non-uniform acceleration.
- In free fall, gravity is the only force and every object near the Earth has the same constant acceleration, whatever its mass. When air resistance matters, see terminal velocity.
Common mistakes
- Giving a displacement or velocity without a direction.
- Using distance for average velocity, or displacement for average speed.
- Using the final velocity instead of the change in velocity when finding acceleration.
- Reading a horizontal velocity–time line as “at rest”. It means uniform velocity unless it is on the time axis.
- Counting area below the time axis as positive when finding displacement.
- Saying the acceleration is zero at the highest point of a throw. Only the velocity is zero there.
- Counting dots instead of gaps on a ticker tape.