IGCSE Physics Speed, Velocity & Acceleration Notes
Speed, velocity and acceleration describe motion. Learn the equations and how to read the two motion graphs and these become quick marks.
Key concepts
- Speed
- Distance travelled per unit time (m/s). A scalar — no direction.
- Velocity
- Speed in a given direction (m/s). A vector — direction matters.
- Acceleration
- The rate of change of velocity (m/s²). Deceleration is negative acceleration.
- On a distance–time graph, a steeper line means a higher speed; a flat line means stationary.
- On a velocity–time graph, the gradient is acceleration and the area under the line is distance travelled.
- Average speed = total distance ÷ total time.
Key formulas
Speed
v = s ÷ t
speed = distance ÷ time.
Acceleration
a = (v − u) ÷ t
u = initial velocity, v = final velocity.
Equation of motion
v² = u² + 2as
links velocity and distance.
Worked example
A car speeds up from 5 m/s to 25 m/s in 4 s. Find its acceleration.
- 1Write the equation: a = (v − u) ÷ t.
- 2Substitute: a = (25 − 5) ÷ 4.
- 3Work out the top: a = 20 ÷ 4.
- 4Calculate: a = 5 m/s².
Answer: a = 5 m/s²
Common mistakes
✗ Using speed instead of change in velocity in the acceleration equation.
✓ Acceleration uses (v − u), the change in velocity.
✗ Reading the gradient of a distance–time graph as acceleration.
✓ On a distance–time graph the gradient is speed, not acceleration.
✗ Forgetting the area under a velocity–time graph gives distance.
✓ Split the area into triangles and rectangles and add them up.
Quick check
Try these, then reveal the answers.
What quantity does the area under a velocity–time graph give?Reveal answer
The distance travelled.
A runner covers 100 m in 20 s. What is the average speed?Reveal answer
5 m/s
Is velocity a scalar or a vector?Reveal answer
A vector — it has direction.
Exam tips
- Check which graph you have before reading a gradient — the meaning differs.
- Show the equation and substitution clearly to secure method marks.
- For distance from a velocity–time graph, calculate the area, not the gradient.
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Frequently asked questions
How do I find distance from a velocity–time graph?+
Calculate the area between the line and the time axis — split it into simple shapes and add them.
What does a horizontal line on a distance–time graph mean?+
The object is stationary — distance is not changing over time.
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