This set covers the five lessons of motion and graphs: speed over a segment, reading two kinds of graph, acceleration, area under a speed-time graph, and displacement. All data are invented for practice.
Attempt each question with the answer closed. Write the unit with every answer, then open the working and compare method, not only the number.
Questions
Q1. A trolley travels 450 m in 90 s. Find its speed.
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Speed = distance ÷ time = 450 ÷ 90 = 5 m/s.
Q2. A bus moves at 90 km/h. Convert this to m/s.
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90 km/h = 90 000 m ÷ 3600 s = 25 m/s. Or 90 ÷ 3.6 = 25 m/s.
Q3. A robot moves at a steady 12 m/s for 2.5 minutes. How far does it travel?
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Convert the time: 2.5 minutes = 150 s. Distance = speed × time = 12 × 150 = 1800 m.
Q4. A distance-time graph has straight sections through these points: (0 s, 0 m), (10 s, 40 m), (20 s, 40 m), (30 s, 100 m). Find the speed in each section and the average speed for the whole 30 s.
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0 to 10 s: 40 ÷ 10 = 4 m/s.
10 to 20 s: distance unchanged, so 0 m/s (at rest).
20 to 30 s: (100 − 40) ÷ 10 = 6 m/s.
Whole journey: 100 ÷ 30 = 3.33 m/s (3 significant figures). Averaging the three speeds gives the same value here only because each section lasts 10 s. That shortcut fails when the times differ.
Q5. On a speed-time graph, a student sees a horizontal line at 8 m/s and says “the object is not moving”. Explain the error and say what the line does show.
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The vertical axis is speed, so a height of 8 m/s means the object is moving at 8 m/s. A horizontal line means the speed is constant, so acceleration is zero. The object would be at rest only if the line lay at 0 m/s.
Q6. A car’s speed rises from 6 m/s to 30 m/s in 8 s. Find its acceleration.
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Change in speed = 30 − 6 = 24 m/s. Acceleration = 24 ÷ 8 = 3 m/s².
Q7. A cyclist slows from 20 m/s to rest in 5 s. Find the acceleration and describe it.
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Change in speed = 0 − 20 = −20 m/s. Acceleration = −20 ÷ 5 = −4 m/s². The cyclist decelerates at 4 m/s².
Q8. A speed-time graph shows speed rising from 0 to 10 m/s in 4 s, staying at 10 m/s for 6 s, then falling to 0 in 2 s. Find the total distance and the average speed.
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Rising triangle: ½ × 4 × 10 = 20 m.
Constant section: 6 × 10 = 60 m.
Falling triangle: ½ × 2 × 10 = 10 m.
Total distance = 20 + 60 + 10 = 90 m. Total time = 4 + 6 + 2 = 12 s. Average speed = 90 ÷ 12 = 7.5 m/s.
Q9. A cyclist rides 500 m east, then 800 m west, in 260 s in total. Find the distance, the displacement, the average speed and the average velocity.
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Distance = 500 + 800 = 1300 m.
Displacement = 500 − 800 = −300 m, which is 300 m west.
Average speed = 1300 ÷ 260 = 5 m/s.
Average velocity = 300 ÷ 260 = 1.15 m/s west (3 significant figures).
Q10. An object starts at 2 m/s and accelerates at a constant 1.5 m/s² for 8 s. Find its final speed and the distance covered. Check the distance by a second method.
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Change in speed = 1.5 × 8 = 12 m/s. Final speed = 2 + 12 = 14 m/s.
Distance using a trapezium: ½ × (2 + 14) × 8 = 64 m.
Check: average speed = (2 + 14) ÷ 2 = 8 m/s, and 8 × 8 = 64 m. Another check splits the area into a rectangle (2 × 8 = 16 m) and a triangle (½ × 8 × 12 = 48 m): 16 + 48 = 64 m.
Q11. A speed-time graph rises in a straight line from 0 to 6 m/s over 4 s. A student says the area under it is 6 × 4 = 24 m. Find the error and give the right distance.
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The area under a sloping line from zero is a triangle, so it needs the ½: ½ × 4 × 6 = 12 m. The student used a rectangle at the final speed, which overstates the distance. Check with the average speed: 3 m/s × 4 s = 12 m.
If you got these wrong
- Q1 to Q3, or units going wrong: revise calculating speed over a segment.
- Q4 or Q5, confusing what a line means: revisit comparing distance-time and speed-time graphs.
- Q6, Q7 or Q10, acceleration and sign mistakes: go to finding acceleration from a gradient.
- Q8, Q10 or Q11, area and distance errors: review interpreting area under a speed-time graph.
- Q9, direction and vectors: study distinguishing displacement from total distance.
The graph-model and residual explorer and the rate and energy graph interpreter help with reading graphs, and the mistake log and retest queue helps you note each error and retest it later. Back to the module overview: motion and graphs.
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