Course: Combined Science + Separate Physics | Tier: Foundation + Higher | Linked: Motion graphs notes · Acceleration questions
✏️ You need: 3 sheets of A4 graph paper (one per task – stick them into your book afterwards), a sharp pencil, a ruler and a calculator. Draw every graph before opening any answers.
📌 KEY DEFINITIONS – learn them word for word
Acceleration is how quickly the speed changes. Unit: m/s².
Line going up = speeding up (accelerating). Flat line = constant speed. Line going down = slowing down (decelerating).
The area under the graph = the distance travelled.
How to draw the graph
- Turn a sheet of A4 graph paper landscape (long side along the bottom). The big squares are 1 cm. Each big square has small 2 mm squares inside it.
- Draw the axes with a ruler, about 2 cm in from the bottom and left edges. Time (s) goes along the bottom. Speed (m/s) goes up the side.
- Use the 📏 scale given for each task. Only number the big 1 cm lines.
- Plot the points from the table as small crosses.
- Join the crosses with straight lines using a ruler.
- Label the three parts A (speeding up), B (constant speed) and C (slowing down).
🔍 See examples of this shape of graph
🧮 Two rules you need
Rule 1 – Acceleration
Step 1: How much did the speed change? (bigger speed − smaller speed)
Step 2: Divide by the time it took.
Acceleration = change in speed ÷ time
Slowing down? Do exactly the same – the answer is called the deceleration.
Rule 2 – Distance (the area under the line)
Split the shape under your line into pieces.
Rectangle: time across × speed up
Triangle: time across × speed up, then ÷ 2 (a triangle is half a rectangle)
Add the pieces together to get the total distance.
Task 1: The bus between two stops 🚌
A bus pulls away from a bus stop. It speeds up for 5 seconds until it reaches 10 m/s. It then travels at a constant speed of 10 m/s for 20 seconds. Finally the driver brakes and the bus slows down, stopping at the next bus stop 5 seconds later.
| Time (s) | 0 | 5 | 25 | 30 |
| Speed (m/s) | 0 | 10 | 10 | 0 |
📏 Scale for Task 1:
Time (along the bottom): 1 big square = 2 s. Number the big lines 0, 2, 4, 6 … up to 30. The axis is 15 cm long.
Speed (up the side): 1 big square = 1 m/s. Number the big lines 0 to 12.
Tip: 5 s is halfway between the 4 and the 6 lines.
Draw the graph, then answer:
Q1 Work out the acceleration of the bus in part A.
Show answer
Change in speed = 10 − 0 = 10 m/s
Time = 5 s
Acceleration = 10 ÷ 5 = 2 m/s²
Q2 What is the acceleration in part B? How can you tell from the graph?
Show answer
0 m/s². The line is flat, so the speed is not changing.
Q3 Work out the deceleration of the bus in part C.
Show answer
Change in speed = 10 − 0 = 10 m/s (it slows from 10 m/s to 0)
Time = 5 s
Deceleration = 10 ÷ 5 = 2 m/s²
Q4 Work out the distance travelled in part A, part B and part C.
Show answer
A (triangle): 5 × 10 = 50, then ÷ 2 = 25 m
B (rectangle): 20 × 10 = 200 m
C (triangle): 5 × 10 = 50, then ÷ 2 = 25 m
Q5 How far apart are the two bus stops?
Show answer
25 + 200 + 25 = 250 m
Task 2: The cyclist at the traffic lights 🚲
The lights turn green. A cyclist speeds up from 0 to 6 m/s in 3 seconds. She rides at 6 m/s for 10 seconds. The next lights turn red, so she brakes and stops in 2 seconds.
| Time (s) | 0 | 3 | 13 | 15 |
| Speed (m/s) | 0 | 6 | 6 | 0 |
📏 Scale for Task 2:
Time (along the bottom): 1 big square = 1 s. Number the big lines 0 to 16.
Speed (up the side): 2 big squares = 1 m/s. Number every second big line 0, 1, 2 … up to 7.
Q6 Work out her acceleration while she speeds up.
Show answer
Change in speed = 6 − 0 = 6 m/s
Time = 3 s
Acceleration = 6 ÷ 3 = 2 m/s²
Q7 Work out her deceleration while she brakes. Look at your graph – which line is steeper, speeding up or braking?
Show answer
Change in speed = 6 m/s. Time = 2 s.
Deceleration = 6 ÷ 2 = 3 m/s²
The braking line is steeper, because her speed changes faster.
Q8 How far is it between the two sets of traffic lights?
Show answer
Speeding up (triangle): 3 × 6 = 18, ÷ 2 = 9 m
Constant speed (rectangle): 10 × 6 = 60 m
Braking (triangle): 2 × 6 = 12, ÷ 2 = 6 m
Total = 9 + 60 + 6 = 75 m
Task 3: The 100 m sprint 🏃
A sprinter starts from 0 and speeds up to 10 m/s in 4 seconds. She runs at 10 m/s until she crosses the finish line at 12 seconds. After the line she slows down and stops at 17 seconds.
Make your own table this time: fill in the speeds at 0 s, 4 s, 12 s and 17 s.
Check your table
Time (s): 0, 4, 12, 17 · Speed (m/s): 0, 10, 10, 0
📏 Scale for Task 3:
Time (along the bottom): 1 big square = 1 s. Number the big lines 0 to 20.
Speed (up the side): 1 big square = 1 m/s. Number the big lines 0 to 12.
Q9 Work out her acceleration at the start.
Show answer
Change in speed = 10 m/s. Time = 4 s.
Acceleration = 10 ÷ 4 = 2.5 m/s²
Q10 Use the area under your graph to check that the race really is 100 m.
Show answer
Speeding up (triangle): 4 × 10 = 40, ÷ 2 = 20 m
Constant speed (rectangle): 8 × 10 = 80 m (from 4 s to 12 s is 8 s)
Total = 20 + 80 = 100 m ✔
Q11 Describe her motion in words. Use the words speeds up, constant speed and slows down.
Show answer
0 to 4 s: she speeds up from 0 to 10 m/s.
4 to 12 s: she runs at a constant speed of 10 m/s.
12 to 17 s: she slows down from 10 m/s to 0.
⚠️ Where students lose marks
- On a speed–time graph a flat line means constant speed – not stopped. Always read the label up the side first.
- Forgetting to ÷ 2 for a triangle.
- Missing units: acceleration is m/s², distance is m.
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