Curriculum fit: GCSE Physics and Combined Science (motion; the equation v² = u² + 2as is mainly Higher). US: middle and high school physical science (motion and stability).
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What Is It?
Speed tells you how fast an object is moving. Velocity is speed in a given direction, so it is a vector. Acceleration is how quickly velocity changes.
Distance–time and velocity–time graphs show motion clearly, and the gradient of each graph has a meaning.
Key Formulas and Ideas
- Speed = distance ÷ time.
- Acceleration = change in velocity ÷ time, or a = (v − u) ÷ t.
- Gradient of a distance–time graph = speed. Gradient of a velocity–time graph = acceleration.
- v² = u² + 2as (constant acceleration).
Worked Examples
Speed
A runner covers 120 m in 20 s. Find the speed.
- Speed = distance ÷ time.
- 120 ÷ 20 = 6.
✓ Answer 6 m/s
Acceleration
A bike speeds up from 0 to 20 m/s in 5 s. Find the acceleration.
- a = (v − u) ÷ t.
- (20 − 0) ÷ 5 = 4.
✓ Answer 4 m/s²
V² = u² + 2as
A car accelerates from rest at 2 m/s² over 25 m. Find its final speed.
- v² = 0 + 2 × 2 × 25 = 100.
- v = √100 = 10.
✓ Answer 10 m/s
Common Mistakes to Avoid
- Confusing speed with velocity.
- Reading a distance–time graph as if it showed speed directly (speed is the gradient).
- Forgetting that deceleration is a negative acceleration.
- Using km/h with m/s in the same calculation.
Practice Questions
Frequently Asked Questions
Can acceleration be negative?
Yes. A negative acceleration (deceleration) means the object is slowing down in the direction it is moving.
What does a horizontal line on a distance–time graph mean?
The object is stationary, because its distance is not changing.
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Reviewed by StudyMorrow editorial review on 5 Nov 2026.