AQA GCSE PHYSICS · PAPER 2 · FOUNDATION & HIGHER
Distance, displacement, speed and velocity
Forces · Lesson 10 of 20
Teacher copy - includes the notes for whoever is teaching from it.
Warm-up
Answer each one, then check.
1. What is the unit of speed?
Metres per second (m/s)
2. What is speed?
How fast something moves
3. What is a vector?
A quantity with size and direction
4. What is a scalar?
A quantity with size only
5. Convert 2 minutes to seconds.
120 s
Learning Objectives
1. Distinguish distance (scalar) from displacement (vector).
2. Distinguish speed from velocity.
3. Recall typical speeds and use a speed = distance ÷ time.
4. Recall and apply s = vt and calculate average speed.
5. Explain qualitatively that circular motion has constant speed but changing velocity (Higher tier).
Speed And Velocity
distance travelled = speed × time s = vt
Distance and speed are scalars. Displacement and velocity are vectors: velocity is speed in a given direction.
Distance and Displacement
|
Displacement is the straight-line distance with its direction. |
A path of 3 km east then 4 km north, with distance 7 km and displacement 5 km in a straight line.
Typical Speeds
Learn these values.
|
Motion |
Typical speed (m/s) |
|---|---|
|
Walking |
1.5 |
|
Running |
3 |
|
Cycling |
6 |
|
Car |
25 |
|
Train |
55 |
|
Plane |
250 |
|
Sound in air |
330 |
Distance from Speed
|
A runner travels at 3.0 m/s for 2.0 minutes. How far do they run? |
1. Convert time
2.0 min = 120 s
2. Substitute
s = vt = 3.0 × 120
3. Answer
s = 360 m
Answer: 360 m
Average Speed
|
A cyclist travels 1500 m in 5.0 minutes. Calculate the average speed. |
1. Convert time
5.0 min = 300 s
2. Rearrange
v = s ÷ t
3. Answer
v = 1500 ÷ 300 = 5.0 m/s
Answer: 5.0 m/s
Distance and Displacement
|
A person walks 3 km east then 4 km north. Find the distance travelled and the displacement. |
1. Distance
3 + 4 = 7 km
2. Displacement
√(3² + 4²) = 5 km
3. Direction
About 53° north of east
Answer: Distance 7 km; displacement 5 km at 53° north of east.
Circular Motion (Higher)
|
A car drives round a roundabout at a constant 10 m/s. Explain whether its velocity is constant. |
1. Speed
Constant at 10 m/s
2. Direction
The direction of travel keeps changing
3. Velocity
A vector, so a change in direction is a change in velocity
Answer: The speed is constant but the velocity changes because the direction changes.
Practical Measurement
Measure speed.
▸ Measure. Use a ruler or tape measure for distance and a stopwatch (or light gates) for time.
▸ Average speed. Total distance divided by total time.
▸ Non-uniform motion. Real motion rarely has constant speed, so calculate an average.
▸ Variation. Speed depends on age, terrain, fitness and distance.
Key Terms
|
Distance How far an object moves; a scalar. |
Displacement Distance in a straight line from start to finish with direction; a vector. |
|
Speed Distance travelled per unit time; a scalar. |
Velocity Speed in a given direction; a vector. |
|
Average speed Total distance divided by total time. |
Uniform motion Motion at constant speed in a straight line. |
Your Task: Journey Times
12 minutes
|
A car travels 120 km in 1.5 hours. Calculate its average speed in km/h and in m/s. How long would sound take to travel 660 m? 1. Convert units. 2. Use v = s ÷ t. |
A good answer shows: 80 km/h; 80 ÷ 3.6 = 22 m/s. Sound: t = 660 ÷ 330 = 2.0 s.
Note: Ask how velocity would differ.
Can I...?
☐ Define distance and displacement.
☐ Define speed and velocity.
☐ Use s = vt.
☐ Calculate average speed.
☐ Recall typical speeds.
☐ Convert units.
☐ Explain circular motion.
☐ Give direction for a vector.
Summary
✓ s = vt.
✓ Displacement and velocity are vectors.
✓ Speed of sound in air about 330 m/s.
✓ Circular motion: constant speed, changing velocity.
|
EXAM FOCUS A runner travels at 3.0 m/s for 120 s. Calculate the distance. (2 marks) Multiply speed by time. |
Exam Practice: Distance, displacement, speed and velocity
Answer all questions. Use the mark allocation as a guide to how much to write. · 14 minutes
▸ Question 1 · 2 marks · Calculate. A runner travels at a steady speed of 3.0 m/s for 120 s. Calculate the distance travelled. Use the equation: distance travelled = speed ×…
▸ Question 2 · 3 marks · Calculate. A cyclist travels 1500 m in 5.0 minutes. Calculate the average speed in m/s.
▸ Question 3 · 2 marks · Explain. Explain the difference between distance and displacement.
▸ Question 4 · 3 marks · Calculate. A person walks 3 km east and then 4 km north. Calculate (a) the distance travelled (b) the magnitude of the displacement.
▸ Question 5 · 3 marks · Explain. A car travels round a roundabout at a constant speed. Explain why its velocity is changing.
Question 1 · 2 marks · Calculate
|
“A runner travels at a steady speed of 3.0 m/s for 120 s. Calculate the distance travelled. Use the equation: distance travelled = speed × time” |
HOW TO ANSWER IT Command word: Calculate. Worth 2 marks, so plan before writing.
Question 1 · mark scheme
2 marks available. Award a mark for each point made.
▸ Correct substitution. 1 mark
▸ 360 m. 1 mark
▸ Model answer. 3.0 × 120 = 360 m
Question 2 · 3 marks · Calculate
|
“A cyclist travels 1500 m in 5.0 minutes. Calculate the average speed in m/s.” |
HOW TO ANSWER IT Command word: Calculate. Worth 3 marks, so plan before writing.
Question 2 · mark scheme
3 marks available. Award a mark for each point made.
▸ Converts to 300 s. 1 mark
▸ Correct substitution. 1 mark
▸ 5.0 m/s. 1 mark
▸ Model answer. t = 300 s; v = 1500 ÷ 300 = 5.0 m/s
Question 3 · 2 marks · Explain
|
“Explain the difference between distance and displacement.” |
HOW TO ANSWER IT Command word: Explain. Worth 2 marks, so plan before writing.
Question 3 · mark scheme
2 marks available. Award a mark for each point made.
▸ Distance: how far, no direction. 1 mark
▸ Displacement: straight line with direction. 1 mark
▸ Model answer. Distance is how far an object moves (a scalar). Displacement is the straight-line distance from the start to the finish in a particular direction (a vector).
Question 4 · 3 marks · Calculate
|
“A person walks 3 km east and then 4 km north. Calculate (a) the distance travelled (b) the magnitude of the displacement.” |
HOW TO ANSWER IT Command word: Calculate. Worth 3 marks, so plan before writing.
Question 4 · mark scheme
3 marks available. Award a mark for each point made.
▸ 7 km. 1 mark
▸ Pythagoras. 1 mark
▸ 5 km. 1 mark
▸ Model answer. (a) 7 km. (b) √(3² + 4²) = 5 km.
Question 5 · 3 marks · Explain
|
“A car travels round a roundabout at a constant speed. Explain why its velocity is changing.” |
HOW TO ANSWER IT Command word: Explain. Worth 3 marks, so plan before writing.
Question 5 · mark scheme
3 marks available. Award a mark for each point made.
▸ Velocity is a vector. 1 mark
▸ Direction changes. 1 mark
▸ So velocity changes with constant speed. 1 mark
▸ Model answer. Velocity is speed in a given direction. The car's direction keeps changing, so its velocity changes even though the speed is constant.