Distance, Displacement and Speed (Part 1/3) Revision Notes | GCSE AQA Higher Physics

1. Why Motion Matters

You walk to school, run for the bus, cycle to meet friends. Every day you're moving — but how do we describe motion scientifically? There's more to it than just 'fast' or 'slow'.

When a footballer kicks a ball towards goal, we need to know more than just how fast it's moving. We need to know which direction it's heading. When a delivery driver calculates fuel costs, they care about the total distance travelled, not just the straight-line distance to the destination.

Physics gives us precise language to describe motion. This isn't just academic — GPS systems, sports analysis, and traffic planning all depend on understanding the difference between distance, displacement, and speed. Let's unlock these concepts step by step.

2. Distance vs Displacement

Picture yourself walking around a rectangular football pitch. You start at one corner and walk all the way around back to where you started. You've covered a lot of ground, but where are you now compared to where you began?

In our football pitch example, if each side is 100m long, you've walked a total distance of 400m. Distance always adds up — every step you take increases the total distance travelled. It can never be negative and it never decreases during a journey.

Your displacement after walking around the pitch is zero metres — you're back where you started. The straight-line distance from start to finish is zero, regardless of how far you actually walked. If you'd walked halfway around and stopped, your displacement would be the diagonal distance across the pitch, pointing from start to finish.

3. Scalar vs Vector Quantities

The difference between distance and displacement reveals a fundamental distinction in physics. Some quantities need direction to make sense, others don't. This isn't just academic — it affects how we calculate and combine these quantities.

When you say 'I ran 5 kilometres', that's distance — a scalar. When you say 'I ran 5 kilometres north-east', that's displacement — a vector. The direction matters because it tells us exactly where you ended up relative to your starting point.

**Trap**: Many students think displacement is always smaller than distance. Actually, they're only equal when you travel in a perfectly straight line. Usually, displacement is smaller because it ignores the twists and turns of your actual path.

4. Understanding Speed

Speed tells us how quickly something moves, but it's more nuanced than you might think. When you check your speedometer while driving, it shows your speed at that exact moment. But your average speed for the whole journey might be very different.

The speed of moving objects is rarely constant. When you walk to school, you might start slowly, speed up to cross a road quickly, slow down to chat with friends, then hurry when you realise you're late. Your speedometer reading changes constantly as you accelerate and brake.

Several factors affect how fast a person can move. Age matters — younger people generally move faster than older people. Fitness level is crucial — trained athletes can maintain higher speeds for longer. The terrain makes a difference too — you'll move faster on flat pavement than up a steep hill. Even the distance matters — you can sprint faster than you can maintain during a marathon.

For exam purposes, you need to know typical speeds for different activities. These aren't exact — they're reasonable estimates that help with calculations and give you a sense of scale when checking your answers.

• Walking: approximately 1.5 m/s
• Running: approximately 3 m/s
• Cycling: approximately 6 m/s

5. Calculating with Speed

Speed calculations appear in every physics exam, but they're straightforward once you know the method. The key is being systematic about units and showing your working clearly for method marks.

Worked example: Calculating Average Speed

A cyclist travels 1200m in 200s. Calculate their average speed. [3 marks]

1. $\text{speed} = \frac{\text{distance}}{\text{time}}$ — [1 mark] Always start with the correct formula
2. $\text{speed} = \frac{1200\text{ m}}{200\text{ s}}$ — [1 mark] Include units with your values
3. $\text{speed} = 6\text{ m/s}$ — [1 mark] Don't forget units in your final answer

Answer: 6 m/s

Notice how this matches our typical cycling speed of 6 m/s. This is a good sanity check — if you calculated 60 m/s or 0.6 m/s, you'd know something was wrong. Always ask yourself: 'Does this answer make sense?'

**Trap**: Students often forget units or mix up the formula. Remember that speed equals distance divided by time, not time divided by distance. If your answer has units of s/m instead of m/s, you've flipped the fraction.

6. Exam Technique and Common Mistakes

Motion questions are mark-winners if you follow the method, but they're also where students make careless errors. The key is being systematic and checking your work makes physical sense.

For calculation questions, always start by writing the formula. This gets you a method mark even if your arithmetic goes wrong later. Then substitute your values with units — this shows the examiner you understand what each number represents. Finally, calculate your answer and include units.

When describing motion, use precise scientific language. Don't say 'how far something goes' — say 'distance travelled'. Don't say 'which way it's pointing' — say 'direction'. The examiner is looking for specific terminology that shows you understand the concepts.

For vector quantities like displacement, you must include direction in your answer. Saying 'displacement = 50m' is incomplete — you need 'displacement = 50m north' or '50m at 30° to the horizontal'. The direction is half the answer for vector quantities.