GCSE Physics Speed, Velocity & Acceleration Notes
Speed is how fast; velocity adds direction; acceleration is how quickly velocity changes. Master the equations and the two motion graphs and you're set.
Key concepts
- Speed and velocity
- Speed is distance travelled per second (scalar). Velocity is speed in a stated direction (vector).
- Acceleration
- The rate of change of velocity, in m/s². Negative acceleration (deceleration) means slowing down.
- Motion graphs
- On a distance–time graph the gradient is speed. On a velocity–time graph the gradient is acceleration and the area under the line is distance.
- Typical walking speed is about 1.5 m/s; running about 3 m/s; cycling about 6 m/s.
- A steeper distance–time graph means a faster speed; a horizontal line means stationary.
- The area under a velocity–time graph gives the distance travelled.
Key formulas
Speed
v = s ÷ t
speed (m/s) = distance (m) ÷ time (s).
Acceleration
a = Δv ÷ t
change in velocity ÷ time taken.
Equation of motion
v² = u² + 2as
final² = initial² + 2 × acceleration × distance.
Worked example
A car speeds up from 10 m/s to 30 m/s in 5 s. Find its acceleration.
- 1Write the equation: a = Δv ÷ t.
- 2Find the change in velocity: Δv = 30 − 10 = 20 m/s.
- 3Substitute: a = 20 ÷ 5.
- 4Calculate: a = 4 m/s².
Answer: a = 4 m/s²
Common mistakes
✗ Reading the area of a distance–time graph as distance.
✓ On a distance–time graph the gradient is speed; area has no meaning. Area is distance only on a velocity–time graph.
✗ Forgetting direction when asked for velocity.
✓ Velocity is a vector — always state the direction.
✗ Using change in velocity as final velocity.
✓ Acceleration uses Δv = final − initial velocity.
Quick check
Try these, then reveal the answers.
What does the gradient of a distance–time graph represent?Reveal answer
Speed.
A runner covers 100 m in 20 s. Find the average speed.Reveal answer
v = 100 ÷ 20 = 5 m/s
What does the area under a velocity–time graph give?Reveal answer
The distance travelled.
Exam tips
- State whether a graph is distance–time or velocity–time before you interpret it.
- For gradient questions, use a large triangle to read values accurately.
- Watch for 'from rest' — it means the initial velocity u = 0.
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Frequently asked questions
What is the difference between speed and velocity?+
Speed is how fast an object moves (a scalar); velocity is speed in a stated direction (a vector), so it can be negative or change even at constant speed.
How do you find distance from a velocity–time graph?+
Calculate the area under the line — split it into rectangles and triangles if needed and add the areas together.
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