This set covers speed units, distance-time graphs, speed-time graphs, density and average rates. Questions run from easy to harder, and every answer is fully worked.
Attempt each question on paper first, then open the answer. Write your units on every line. Aim to find the errors rather than to finish quickly.
Questions
1. Convert 54 km/h to m/s.
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54 ÷ 3.6 = 15 m/s. Check: 15 × 3.6 = 54.
2. Convert 25 m/s to km/h.
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25 × 3.6 = 90 km/h. Check: 90 ÷ 3.6 = 25.
3. A sprinter runs 100 m in 12.5 s. Find the speed in m/s and in km/h.
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Speed = 100 ÷ 12.5 = 8 m/s. In km/h: 8 × 3.6 = 28.8 km/h.
4. Convert 0.25 km/min to m/s, giving the answer to 3 significant figures.
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0.25 km = 250 m and 1 min = 60 s, so 250 ÷ 60 = 4.1666… = 4.17 m/s. Check: 0.25 × 60 = 15 km/h, and 15 ÷ 3.6 = 4.1666…
5. A distance-time graph has turning points (time in hours, distance in km): (0, 0), (1, 20), (2, 20), (4, 50). Find the speed in each part, then the average speed for the whole trip.
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0 to 1 h: 20 ÷ 1 = 20 km/h. 1 h to 2 h: no change in distance, so 0 km/h. 2 h to 4 h: (50 − 20) ÷ (4 − 2) = 30 ÷ 2 = 15 km/h. Average: 50 ÷ 4 = 12.5 km/h.
6. A driver goes 90 km at 45 km/h, then returns 90 km at 30 km/h. Find the average speed for the round trip.
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Times: 90 ÷ 45 = 2 h and 90 ÷ 30 = 3 h. Total distance 180 km, total time 5 h. Average = 180 ÷ 5 = 36 km/h. The simple mean of 45 and 30 would be 37.5, which is the wrong answer.
7. A speed-time graph rises steadily from 0 to 15 m/s in 5 s, stays at 15 m/s for 8 s, then falls steadily to 0 in 7 s. Find the total distance and the average speed.
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First triangle: ½ × 5 × 15 = 37.5 m. Rectangle: 8 × 15 = 120 m. Last triangle: ½ × 7 × 15 = 52.5 m. Total = 37.5 + 120 + 52.5 = 210 m. Total time = 5 + 8 + 7 = 20 s. Average speed = 210 ÷ 20 = 10.5 m/s. Check with a trapezium: ½ × (20 + 8) × 15 = 210.
8. A block 8 cm by 5 cm by 2.5 cm has mass 620 g. Find the density in g/cm³.
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Volume = 8 × 5 × 2.5 = 100 cm³. Density = 620 ÷ 100 = 6.2 g/cm³.
9. A liquid has density 0.9 g/cm³. Find the mass of 3.5 litres in kg.
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3.5 litres = 3500 cm³. Mass = 0.9 × 3500 = 3150 g = 3.15 kg.
10. Aluminium has density 2700 kg/m³. Give this in g/cm³.
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Divide by 1000: 2700 ÷ 1000 = 2.7 g/cm³. Check: 2.7 × 1000 = 2700.
11. A train travels at a constant 60 km/h for 45 minutes. Find the distance in km.
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45 min = 0.75 h. Distance = 60 × 0.75 = 45 km.
12. A car’s distance is s = t² metres after t seconds. Find the average speed from t = 2 to t = 5.
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At t = 5, s = 25. At t = 2, s = 4. Change in distance = 21 m in 3 s. Average speed = 21 ÷ 3 = 7 m/s.
If you got these wrong
Sort each error into a type, then go back to the lesson for that type.
- Wrong size after a unit change (questions 1, 2, 3, 4, 11): see converting a compound speed unit.
- Wrong speed from a graph segment, or a stop misread (question 5): see reading a distance-time graph.
- Wrong distance or acceleration from a speed-time graph (question 7): see the area under a speed-time graph.
- Answer a thousand times off in density (questions 8, 9, 10): see calculating density with consistent units.
- Averaged two speeds, or used one point for a rate (questions 6, 12): see average rate versus instantaneous reading.
Keep a record of your errors in the mistake log and retest queue, and use the non-calculator working trainer and the percentage-base explorer to check method on your own numbers. The study route is on the module page.
If the same error returns after you have reviewed the lesson, online one-to-one Mathematics tuition gives a teacher the chance to see your working and find the cause.