ScienceAges 16-18

Speed-time graphs: area & distance

Calculate total distance travelled from the area under a two-stage speed-time graph (acceleration triangle plus constant-speed rectangle). Review suitability for your learners before teaching.

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Worksheet StudioPractice pack · Ages 16-18

Speed-time graphs: area & distance

Take your time. Show your thinking.

1. On a speed-time graph, a train accelerates uniformly from rest to 32 m/s in 5 s and then continues at a constant speed of 32 m/s for a further 6 s. Calculate the total distance travelled.
v_max = 32 m/s (t₁ = 5 s, t₂ = 6 s) · Distance = Area = ½vt₁ + vt₂
2. On a speed-time graph, a train accelerates uniformly from rest to 14 m/s in 3 s and then continues at a constant speed of 14 m/s for a further 7 s. Calculate the total distance travelled.
v_max = 14 m/s (t₁ = 3 s, t₂ = 7 s) · Distance = Area = ½vt₁ + vt₂
3. On a speed-time graph, a train accelerates uniformly from rest to 28 m/s in 2 s and then continues at a constant speed of 28 m/s for a further 5 s. Calculate the total distance travelled.
v_max = 28 m/s (t₁ = 2 s, t₂ = 5 s) · Distance = Area = ½vt₁ + vt₂
4. On a speed-time graph, a train accelerates uniformly from rest to 44 m/s in 5 s and then continues at a constant speed of 44 m/s for a further 6 s. Calculate the total distance travelled.
v_max = 44 m/s (t₁ = 5 s, t₂ = 6 s) · Distance = Area = ½vt₁ + vt₂
5. On a speed-time graph, a train accelerates uniformly from rest to 46 m/s in 3 s and then continues at a constant speed of 46 m/s for a further 6 s. Calculate the total distance travelled.
v_max = 46 m/s (t₁ = 3 s, t₂ = 6 s) · Distance = Area = ½vt₁ + vt₂
6. On a speed-time graph, a train accelerates uniformly from rest to 46 m/s in 9 s and then continues at a constant speed of 46 m/s for a further 13 s. Calculate the total distance travelled.
v_max = 46 m/s (t₁ = 9 s, t₂ = 13 s) · Distance = Area = ½vt₁ + vt₂
7. On a speed-time graph, a train accelerates uniformly from rest to 22 m/s in 6 s and then continues at a constant speed of 22 m/s for a further 11 s. Calculate the total distance travelled.
v_max = 22 m/s (t₁ = 6 s, t₂ = 11 s) · Distance = Area = ½vt₁ + vt₂
8. On a speed-time graph, a train accelerates uniformly from rest to 28 m/s in 6 s and then continues at a constant speed of 28 m/s for a further 20 s. Calculate the total distance travelled.
v_max = 28 m/s (t₁ = 6 s, t₂ = 20 s) · Distance = Area = ½vt₁ + vt₂
9. On a speed-time graph, a train accelerates uniformly from rest to 50 m/s in 6 s and then continues at a constant speed of 50 m/s for a further 17 s. Calculate the total distance travelled.
v_max = 50 m/s (t₁ = 6 s, t₂ = 17 s) · Distance = Area = ½vt₁ + vt₂
10. On a speed-time graph, a train accelerates uniformly from rest to 8 m/s in 2 s and then continues at a constant speed of 8 m/s for a further 7 s. Calculate the total distance travelled.
v_max = 8 m/s (t₁ = 2 s, t₂ = 7 s) · Distance = Area = ½vt₁ + vt₂
11. On a speed-time graph, a train accelerates uniformly from rest to 16 m/s in 10 s and then continues at a constant speed of 16 m/s for a further 5 s. Calculate the total distance travelled.
v_max = 16 m/s (t₁ = 10 s, t₂ = 5 s) · Distance = Area = ½vt₁ + vt₂
12. On a speed-time graph, a train accelerates uniformly from rest to 30 m/s in 8 s and then continues at a constant speed of 30 m/s for a further 18 s. Calculate the total distance travelled.
v_max = 30 m/s (t₁ = 8 s, t₂ = 18 s) · Distance = Area = ½vt₁ + vt₂

12 questions · Seed 43 · Age guidance, not curriculum certification

View the answer key

Worksheet StudioAnswer key · Ages 16-18

Speed-time graphs: area & distance

Answers and reasoning. Review before teaching.

1. On a speed-time graph, a train accelerates uniformly from rest to 32 m/s in 5 s and then continues at a constant speed of 32 m/s for a further 6 s. Calculate the total distance travelled.
272 m
Distance is the area under the speed-time graph: triangle area = ½ × 5 × 32 = 80 m, plus rectangle area = 6 × 32 = 192 m. Total distance = 80 + 192 = 272 m.
2. On a speed-time graph, a train accelerates uniformly from rest to 14 m/s in 3 s and then continues at a constant speed of 14 m/s for a further 7 s. Calculate the total distance travelled.
119 m
Distance is the area under the speed-time graph: triangle area = ½ × 3 × 14 = 21 m, plus rectangle area = 7 × 14 = 98 m. Total distance = 21 + 98 = 119 m.
3. On a speed-time graph, a train accelerates uniformly from rest to 28 m/s in 2 s and then continues at a constant speed of 28 m/s for a further 5 s. Calculate the total distance travelled.
168 m
Distance is the area under the speed-time graph: triangle area = ½ × 2 × 28 = 28 m, plus rectangle area = 5 × 28 = 140 m. Total distance = 28 + 140 = 168 m.
4. On a speed-time graph, a train accelerates uniformly from rest to 44 m/s in 5 s and then continues at a constant speed of 44 m/s for a further 6 s. Calculate the total distance travelled.
374 m
Distance is the area under the speed-time graph: triangle area = ½ × 5 × 44 = 110 m, plus rectangle area = 6 × 44 = 264 m. Total distance = 110 + 264 = 374 m.
5. On a speed-time graph, a train accelerates uniformly from rest to 46 m/s in 3 s and then continues at a constant speed of 46 m/s for a further 6 s. Calculate the total distance travelled.
345 m
Distance is the area under the speed-time graph: triangle area = ½ × 3 × 46 = 69 m, plus rectangle area = 6 × 46 = 276 m. Total distance = 69 + 276 = 345 m.
6. On a speed-time graph, a train accelerates uniformly from rest to 46 m/s in 9 s and then continues at a constant speed of 46 m/s for a further 13 s. Calculate the total distance travelled.
805 m
Distance is the area under the speed-time graph: triangle area = ½ × 9 × 46 = 207 m, plus rectangle area = 13 × 46 = 598 m. Total distance = 207 + 598 = 805 m.
7. On a speed-time graph, a train accelerates uniformly from rest to 22 m/s in 6 s and then continues at a constant speed of 22 m/s for a further 11 s. Calculate the total distance travelled.
308 m
Distance is the area under the speed-time graph: triangle area = ½ × 6 × 22 = 66 m, plus rectangle area = 11 × 22 = 242 m. Total distance = 66 + 242 = 308 m.
8. On a speed-time graph, a train accelerates uniformly from rest to 28 m/s in 6 s and then continues at a constant speed of 28 m/s for a further 20 s. Calculate the total distance travelled.
644 m
Distance is the area under the speed-time graph: triangle area = ½ × 6 × 28 = 84 m, plus rectangle area = 20 × 28 = 560 m. Total distance = 84 + 560 = 644 m.
9. On a speed-time graph, a train accelerates uniformly from rest to 50 m/s in 6 s and then continues at a constant speed of 50 m/s for a further 17 s. Calculate the total distance travelled.
1000 m
Distance is the area under the speed-time graph: triangle area = ½ × 6 × 50 = 150 m, plus rectangle area = 17 × 50 = 850 m. Total distance = 150 + 850 = 1000 m.
10. On a speed-time graph, a train accelerates uniformly from rest to 8 m/s in 2 s and then continues at a constant speed of 8 m/s for a further 7 s. Calculate the total distance travelled.
64 m
Distance is the area under the speed-time graph: triangle area = ½ × 2 × 8 = 8 m, plus rectangle area = 7 × 8 = 56 m. Total distance = 8 + 56 = 64 m.
11. On a speed-time graph, a train accelerates uniformly from rest to 16 m/s in 10 s and then continues at a constant speed of 16 m/s for a further 5 s. Calculate the total distance travelled.
160 m
Distance is the area under the speed-time graph: triangle area = ½ × 10 × 16 = 80 m, plus rectangle area = 5 × 16 = 80 m. Total distance = 80 + 80 = 160 m.
12. On a speed-time graph, a train accelerates uniformly from rest to 30 m/s in 8 s and then continues at a constant speed of 30 m/s for a further 18 s. Calculate the total distance travelled.
660 m
Distance is the area under the speed-time graph: triangle area = ½ × 8 × 30 = 120 m, plus rectangle area = 18 × 30 = 540 m. Total distance = 120 + 540 = 660 m.

12 questions · Seed 43 · Age guidance, not curriculum certification

Worksheet StudioPractice pack · Ages 16-18

Speed-time graphs: area & distance

Take your time. Show your thinking.

1. On a speed-time graph, a train accelerates uniformly from rest to 32 m/s in 5 s and then continues at a constant speed of 32 m/s for a further 6 s. Calculate the total distance travelled.
v_max = 32 m/s (t₁ = 5 s, t₂ = 6 s) · Distance = Area = ½vt₁ + vt₂
2. On a speed-time graph, a train accelerates uniformly from rest to 14 m/s in 3 s and then continues at a constant speed of 14 m/s for a further 7 s. Calculate the total distance travelled.
v_max = 14 m/s (t₁ = 3 s, t₂ = 7 s) · Distance = Area = ½vt₁ + vt₂
3. On a speed-time graph, a train accelerates uniformly from rest to 28 m/s in 2 s and then continues at a constant speed of 28 m/s for a further 5 s. Calculate the total distance travelled.
v_max = 28 m/s (t₁ = 2 s, t₂ = 5 s) · Distance = Area = ½vt₁ + vt₂
4. On a speed-time graph, a train accelerates uniformly from rest to 44 m/s in 5 s and then continues at a constant speed of 44 m/s for a further 6 s. Calculate the total distance travelled.
v_max = 44 m/s (t₁ = 5 s, t₂ = 6 s) · Distance = Area = ½vt₁ + vt₂
5. On a speed-time graph, a train accelerates uniformly from rest to 46 m/s in 3 s and then continues at a constant speed of 46 m/s for a further 6 s. Calculate the total distance travelled.
v_max = 46 m/s (t₁ = 3 s, t₂ = 6 s) · Distance = Area = ½vt₁ + vt₂
6. On a speed-time graph, a train accelerates uniformly from rest to 46 m/s in 9 s and then continues at a constant speed of 46 m/s for a further 13 s. Calculate the total distance travelled.
v_max = 46 m/s (t₁ = 9 s, t₂ = 13 s) · Distance = Area = ½vt₁ + vt₂
7. On a speed-time graph, a train accelerates uniformly from rest to 22 m/s in 6 s and then continues at a constant speed of 22 m/s for a further 11 s. Calculate the total distance travelled.
v_max = 22 m/s (t₁ = 6 s, t₂ = 11 s) · Distance = Area = ½vt₁ + vt₂
8. On a speed-time graph, a train accelerates uniformly from rest to 28 m/s in 6 s and then continues at a constant speed of 28 m/s for a further 20 s. Calculate the total distance travelled.
v_max = 28 m/s (t₁ = 6 s, t₂ = 20 s) · Distance = Area = ½vt₁ + vt₂
9. On a speed-time graph, a train accelerates uniformly from rest to 50 m/s in 6 s and then continues at a constant speed of 50 m/s for a further 17 s. Calculate the total distance travelled.
v_max = 50 m/s (t₁ = 6 s, t₂ = 17 s) · Distance = Area = ½vt₁ + vt₂
10. On a speed-time graph, a train accelerates uniformly from rest to 8 m/s in 2 s and then continues at a constant speed of 8 m/s for a further 7 s. Calculate the total distance travelled.
v_max = 8 m/s (t₁ = 2 s, t₂ = 7 s) · Distance = Area = ½vt₁ + vt₂
11. On a speed-time graph, a train accelerates uniformly from rest to 16 m/s in 10 s and then continues at a constant speed of 16 m/s for a further 5 s. Calculate the total distance travelled.
v_max = 16 m/s (t₁ = 10 s, t₂ = 5 s) · Distance = Area = ½vt₁ + vt₂
12. On a speed-time graph, a train accelerates uniformly from rest to 30 m/s in 8 s and then continues at a constant speed of 30 m/s for a further 18 s. Calculate the total distance travelled.
v_max = 30 m/s (t₁ = 8 s, t₂ = 18 s) · Distance = Area = ½vt₁ + vt₂

12 questions · Seed 43 · Age guidance, not curriculum certification

Worksheet StudioAnswer key · Ages 16-18

Speed-time graphs: area & distance

Answers and reasoning. Review before teaching.

1. On a speed-time graph, a train accelerates uniformly from rest to 32 m/s in 5 s and then continues at a constant speed of 32 m/s for a further 6 s. Calculate the total distance travelled.
272 m
Distance is the area under the speed-time graph: triangle area = ½ × 5 × 32 = 80 m, plus rectangle area = 6 × 32 = 192 m. Total distance = 80 + 192 = 272 m.
2. On a speed-time graph, a train accelerates uniformly from rest to 14 m/s in 3 s and then continues at a constant speed of 14 m/s for a further 7 s. Calculate the total distance travelled.
119 m
Distance is the area under the speed-time graph: triangle area = ½ × 3 × 14 = 21 m, plus rectangle area = 7 × 14 = 98 m. Total distance = 21 + 98 = 119 m.
3. On a speed-time graph, a train accelerates uniformly from rest to 28 m/s in 2 s and then continues at a constant speed of 28 m/s for a further 5 s. Calculate the total distance travelled.
168 m
Distance is the area under the speed-time graph: triangle area = ½ × 2 × 28 = 28 m, plus rectangle area = 5 × 28 = 140 m. Total distance = 28 + 140 = 168 m.
4. On a speed-time graph, a train accelerates uniformly from rest to 44 m/s in 5 s and then continues at a constant speed of 44 m/s for a further 6 s. Calculate the total distance travelled.
374 m
Distance is the area under the speed-time graph: triangle area = ½ × 5 × 44 = 110 m, plus rectangle area = 6 × 44 = 264 m. Total distance = 110 + 264 = 374 m.
5. On a speed-time graph, a train accelerates uniformly from rest to 46 m/s in 3 s and then continues at a constant speed of 46 m/s for a further 6 s. Calculate the total distance travelled.
345 m
Distance is the area under the speed-time graph: triangle area = ½ × 3 × 46 = 69 m, plus rectangle area = 6 × 46 = 276 m. Total distance = 69 + 276 = 345 m.
6. On a speed-time graph, a train accelerates uniformly from rest to 46 m/s in 9 s and then continues at a constant speed of 46 m/s for a further 13 s. Calculate the total distance travelled.
805 m
Distance is the area under the speed-time graph: triangle area = ½ × 9 × 46 = 207 m, plus rectangle area = 13 × 46 = 598 m. Total distance = 207 + 598 = 805 m.
7. On a speed-time graph, a train accelerates uniformly from rest to 22 m/s in 6 s and then continues at a constant speed of 22 m/s for a further 11 s. Calculate the total distance travelled.
308 m
Distance is the area under the speed-time graph: triangle area = ½ × 6 × 22 = 66 m, plus rectangle area = 11 × 22 = 242 m. Total distance = 66 + 242 = 308 m.
8. On a speed-time graph, a train accelerates uniformly from rest to 28 m/s in 6 s and then continues at a constant speed of 28 m/s for a further 20 s. Calculate the total distance travelled.
644 m
Distance is the area under the speed-time graph: triangle area = ½ × 6 × 28 = 84 m, plus rectangle area = 20 × 28 = 560 m. Total distance = 84 + 560 = 644 m.
9. On a speed-time graph, a train accelerates uniformly from rest to 50 m/s in 6 s and then continues at a constant speed of 50 m/s for a further 17 s. Calculate the total distance travelled.
1000 m
Distance is the area under the speed-time graph: triangle area = ½ × 6 × 50 = 150 m, plus rectangle area = 17 × 50 = 850 m. Total distance = 150 + 850 = 1000 m.
10. On a speed-time graph, a train accelerates uniformly from rest to 8 m/s in 2 s and then continues at a constant speed of 8 m/s for a further 7 s. Calculate the total distance travelled.
64 m
Distance is the area under the speed-time graph: triangle area = ½ × 2 × 8 = 8 m, plus rectangle area = 7 × 8 = 56 m. Total distance = 8 + 56 = 64 m.
11. On a speed-time graph, a train accelerates uniformly from rest to 16 m/s in 10 s and then continues at a constant speed of 16 m/s for a further 5 s. Calculate the total distance travelled.
160 m
Distance is the area under the speed-time graph: triangle area = ½ × 10 × 16 = 80 m, plus rectangle area = 5 × 16 = 80 m. Total distance = 80 + 80 = 160 m.
12. On a speed-time graph, a train accelerates uniformly from rest to 30 m/s in 8 s and then continues at a constant speed of 30 m/s for a further 18 s. Calculate the total distance travelled.
660 m
Distance is the area under the speed-time graph: triangle area = ½ × 8 × 30 = 120 m, plus rectangle area = 18 × 30 = 540 m. Total distance = 120 + 540 = 660 m.

12 questions · Seed 43 · Age guidance, not curriculum certification