Kinematics describes how objects move, using speed, velocity, acceleration and motion graphs. It is the foundation for Dynamics, Forces and Energy, and graph questions appear in almost every Paper 1 and Paper 2.
All motion in this topic is along a straight line, and g is taken as 10 m/s² unless the question says otherwise.
What these notes cover
- •Distance and displacement
- •Speed, velocity and average speed
- •Converting km/h to m/s
- •Acceleration and deceleration
- •Uniform and non-uniform acceleration
- •Distance-time and speed-time graphs
- •Gradient and area under a graph
- •Free fall
- •Three worked examples
- •Six common mistakes
- •Exam technique and summary
Key definitions
- Distance
- The total length of the path travelled, whatever the direction. It is a scalar: it has magnitude only.
- Displacement
- The straight-line distance from the starting point, measured in a stated direction. It is a vector: it has both magnitude and direction.
- Speed
- The distance travelled per unit time. It is a scalar. SI unit: m/s.
- Velocity
- The rate of change of displacement. It is a vector, so always state its direction, for example "12 m/s to the right". SI unit: m/s.
- Acceleration
- The rate of change of velocity. It is a vector. SI unit: m/s².
Key formulas
Speed
v = d ÷ t
d is the distance in metres, t is the time in seconds.
Average speed
average speed = total distance ÷ total time
The total time includes any time spent at rest.
Acceleration
a = (v − u) ÷ t
u is the initial velocity, v is the final velocity. Always subtract final minus initial.
Free fall from rest
v = g t
g ≈ 10 m/s² for every object when air resistance is negligible.
Unit conversion
km/h ÷ 3.6 = m/s
For example, 36 km/h = 10 m/s.
Worked example
A cyclist rides 600 m in 120 s, rests for 60 s, then rides a further 900 m in 120 s. Calculate the average speed of the cyclist for the whole journey.
- 1Find the total distance: 600 + 900 = 1500 m.
- 2Find the total time. The rest time is part of the journey, so it must be counted: 120 + 60 + 120 = 300 s.
- 3Average speed = total distance ÷ total time = 1500 ÷ 300 = 5.0 m/s.
Watch out: The two riding speeds are 5.0 m/s and 7.5 m/s. Averaging them to get 6.25 m/s is wrong. Average speed is always total distance divided by total time.
Common mistakes
Reading a distance-time graph as a speed-time graph
Wrong: "The line on the distance-time graph is horizontal, so the object is moving at constant speed."
Right: On a distance-time graph a horizontal line means the object is at rest. Uniform speed appears as a straight sloping line. A horizontal line means uniform speed only on a speed-time graph.
"Zero velocity means zero acceleration" at the top of a throw
Wrong: "At its highest point the ball stops for an instant, so its acceleration is zero."
Right: The velocity is zero but it is still changing, so the acceleration is not zero. With no air resistance it is 10 m/s² downward on the way up, at the top, and on the way down.
"Heavier objects fall faster"
Wrong: "The steel ball has a larger mass than the rubber ball, so it lands first."
Right: When air resistance is negligible, all objects near the Earth's surface fall with the same acceleration, whatever their mass. Released together from the same height, both balls land together.
Questions students ask
What is the difference between speed and velocity?
Speed is the distance travelled per unit time and is a scalar. Velocity is the rate of change of displacement and is a vector, so it needs a direction. A runner who completes one lap of a 400 m track in 80 s has an average speed of 5 m/s but an average velocity of 0 m/s, because the displacement is zero.
What does the gradient of a speed-time graph represent?
The gradient of a speed-time graph gives the acceleration. The area under a speed-time graph gives the distance travelled. The gradient of a distance-time graph gives the speed.
Is a decreasing acceleration the same as a deceleration?
No. If the acceleration is decreasing but still positive, the object is still getting faster. The object slows down only when the acceleration is in the opposite direction to its motion.
How do you convert km/h to m/s?
Divide by 3.6, because 1 km = 1000 m and 1 h = 3600 s. For example, 36 km/h = 10 m/s. To go from m/s to km/h, multiply by 3.6.
In the full PDF
- •Every section above explained in full, with diagrams
- •How to describe motion from distance-time and speed-time graphs
- •A worked MRT speed-time graph question (acceleration, distance, average speed)
- •A worked free-fall question
- •All six common mistakes, with the wrong and right answers side by side
- •Exam technique checklist and a one-page summary