Distance-Time Graphs

IGCSE Edexcel Physics
1.3–1.4 Speed, distance and distance-time graphs
Key Concepts: Speed = distance ÷ time ($v = d/t$). The gradient of a distance-time graph gives speed. A horizontal line means stationary; a steeper line means greater speed; a curved line means changing speed (acceleration or deceleration).

Section A — Reading Distance-Time Graphs

1. Describe what each of the following lines on a distance-time graph represents. [3]

a) A horizontal line

b) A straight line sloping upward

c) A curved line that becomes steeper

2. Two objects travel the same total distance. Object A takes 20 s and Object B takes 50 s. State which object has greater average speed and explain how you know. [2]
3. Explain how you calculate the speed of an object from a distance-time graph. [2]

Section B — Speed Calculations

4. A student walks 120 m in 80 s. Calculate the average speed. [2]
5. A runner covers 400 m in 50 s. Calculate the average speed. [2]
6. A car travels at $12\,\text{m/s}$ for 30 s. How far does it travel? [2]
7. A distance-time graph shows a straight line from (0, 0) to (50 s, 150 m). Calculate the speed. [2]
8. A jogger travels 360 m in 3 minutes. Calculate the average speed in m/s. [2]

Section C — Applying Graph Skills

9. A distance-time graph has three sections: a straight line of gradient 4 m/s for 10 s, a horizontal section for 5 s, then a straight line of gradient 6 m/s for 10 s. [4]

a) What is the total distance travelled?

b) What is the average speed for the whole journey?

10. A car travels 360 km in 4 hours. Convert this speed to m/s. [3]

Total marks: 24

Mark Scheme

1. a) Object is stationary (distance is not changing) [1]; b) Object is moving at constant speed [1]; c) Object is accelerating (speed is increasing) [1] [3]
2. Object A has greater average speed [1]; because it covers the same distance in less time (speed = d/t, smaller t gives larger v) [1] [2]
3. Calculate the gradient of the line [1]: gradient = change in distance ÷ change in time [1] [2]
4. $v = d/t = 120 \div 80 = 1.5\,\text{m/s}$ [2]
5. $v = 400 \div 50 = 8\,\text{m/s}$ [2]
6. $d = vt = 12 \times 30 = 360\,\text{m}$ [2]
7. $v = 150 \div 50 = 3\,\text{m/s}$ [2]
8. Convert: 3 min = 180 s [1]; $v = 360 \div 180 = 2\,\text{m/s}$ [1] [2]
9. a) Section 1: $4 \times 10 = 40\,\text{m}$; Section 2: 0 m; Section 3: $6 \times 10 = 60\,\text{m}$; Total = 100 m [2]; b) Total time = 25 s; average speed = $100 \div 25 = 4\,\text{m/s}$ [2] [4]
10. Convert km to m: $360\,\text{km} = 360\,000\,\text{m}$ [1]; convert hours to seconds: $4\,\text{h} = 14\,400\,\text{s}$ [1]; $v = 360\,000 \div 14\,400 = 25\,\text{m/s}$ [1] [3]