ScienceAges 13-15

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 13-15

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 2 s and then continues at a constant speed of 32 m/s for a further 10 s. Calculate the total distance travelled.
v_max = 32 m/s (t₁ = 2 s, t₂ = 10 s) · Distance = Area = ½vt₁ + vt₂
2. 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 7 s. Calculate the total distance travelled.
v_max = 46 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 46 m/s in 7 s and then continues at a constant speed of 46 m/s for a further 10 s. Calculate the total distance travelled.
v_max = 46 m/s (t₁ = 7 s, t₂ = 10 s) · Distance = Area = ½vt₁ + vt₂
4. On a speed-time graph, a train accelerates uniformly from rest to 22 m/s in 12 s and then continues at a constant speed of 22 m/s for a further 10 s. Calculate the total distance travelled.
v_max = 22 m/s (t₁ = 12 s, t₂ = 10 s) · Distance = Area = ½vt₁ + vt₂
5. On a speed-time graph, a train accelerates uniformly from rest to 44 m/s in 3 s and then continues at a constant speed of 44 m/s for a further 18 s. Calculate the total distance travelled.
v_max = 44 m/s (t₁ = 3 s, t₂ = 18 s) · Distance = Area = ½vt₁ + vt₂
6. On a speed-time graph, a train accelerates uniformly from rest to 20 m/s in 2 s and then continues at a constant speed of 20 m/s for a further 4 s. Calculate the total distance travelled.
v_max = 20 m/s (t₁ = 2 s, t₂ = 4 s) · Distance = Area = ½vt₁ + vt₂
7. On a speed-time graph, a train accelerates uniformly from rest to 30 m/s in 11 s and then continues at a constant speed of 30 m/s for a further 7 s. Calculate the total distance travelled.
v_max = 30 m/s (t₁ = 11 s, t₂ = 7 s) · Distance = Area = ½vt₁ + vt₂
8. On a speed-time graph, a train accelerates uniformly from rest to 38 m/s in 3 s and then continues at a constant speed of 38 m/s for a further 12 s. Calculate the total distance travelled.
v_max = 38 m/s (t₁ = 3 s, t₂ = 12 s) · Distance = Area = ½vt₁ + vt₂
9. On a speed-time graph, a train accelerates uniformly from rest to 16 m/s in 12 s and then continues at a constant speed of 16 m/s for a further 19 s. Calculate the total distance travelled.
v_max = 16 m/s (t₁ = 12 s, t₂ = 19 s) · Distance = Area = ½vt₁ + vt₂
10. On a speed-time graph, a train accelerates uniformly from rest to 34 m/s in 10 s and then continues at a constant speed of 34 m/s for a further 16 s. Calculate the total distance travelled.
v_max = 34 m/s (t₁ = 10 s, t₂ = 16 s) · Distance = Area = ½vt₁ + vt₂
11. On a speed-time graph, a train accelerates uniformly from rest to 32 m/s in 4 s and then continues at a constant speed of 32 m/s for a further 13 s. Calculate the total distance travelled.
v_max = 32 m/s (t₁ = 4 s, t₂ = 13 s) · Distance = Area = ½vt₁ + vt₂
12. On a speed-time graph, a train accelerates uniformly from rest to 10 m/s in 2 s and then continues at a constant speed of 10 m/s for a further 9 s. Calculate the total distance travelled.
v_max = 10 m/s (t₁ = 2 s, t₂ = 9 s) · Distance = Area = ½vt₁ + vt₂

12 questions · Seed 47 · Age guidance, not curriculum certification

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Worksheet StudioAnswer key · Ages 13-15

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 2 s and then continues at a constant speed of 32 m/s for a further 10 s. Calculate the total distance travelled.
352 m
Distance is the area under the speed-time graph: triangle area = ½ × 2 × 32 = 32 m, plus rectangle area = 10 × 32 = 320 m. Total distance = 32 + 320 = 352 m.
2. 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 7 s. Calculate the total distance travelled.
391 m
Distance is the area under the speed-time graph: triangle area = ½ × 3 × 46 = 69 m, plus rectangle area = 7 × 46 = 322 m. Total distance = 69 + 322 = 391 m.
3. On a speed-time graph, a train accelerates uniformly from rest to 46 m/s in 7 s and then continues at a constant speed of 46 m/s for a further 10 s. Calculate the total distance travelled.
621 m
Distance is the area under the speed-time graph: triangle area = ½ × 7 × 46 = 161 m, plus rectangle area = 10 × 46 = 460 m. Total distance = 161 + 460 = 621 m.
4. On a speed-time graph, a train accelerates uniformly from rest to 22 m/s in 12 s and then continues at a constant speed of 22 m/s for a further 10 s. Calculate the total distance travelled.
352 m
Distance is the area under the speed-time graph: triangle area = ½ × 12 × 22 = 132 m, plus rectangle area = 10 × 22 = 220 m. Total distance = 132 + 220 = 352 m.
5. On a speed-time graph, a train accelerates uniformly from rest to 44 m/s in 3 s and then continues at a constant speed of 44 m/s for a further 18 s. Calculate the total distance travelled.
858 m
Distance is the area under the speed-time graph: triangle area = ½ × 3 × 44 = 66 m, plus rectangle area = 18 × 44 = 792 m. Total distance = 66 + 792 = 858 m.
6. On a speed-time graph, a train accelerates uniformly from rest to 20 m/s in 2 s and then continues at a constant speed of 20 m/s for a further 4 s. Calculate the total distance travelled.
100 m
Distance is the area under the speed-time graph: triangle area = ½ × 2 × 20 = 20 m, plus rectangle area = 4 × 20 = 80 m. Total distance = 20 + 80 = 100 m.
7. On a speed-time graph, a train accelerates uniformly from rest to 30 m/s in 11 s and then continues at a constant speed of 30 m/s for a further 7 s. Calculate the total distance travelled.
375 m
Distance is the area under the speed-time graph: triangle area = ½ × 11 × 30 = 165 m, plus rectangle area = 7 × 30 = 210 m. Total distance = 165 + 210 = 375 m.
8. On a speed-time graph, a train accelerates uniformly from rest to 38 m/s in 3 s and then continues at a constant speed of 38 m/s for a further 12 s. Calculate the total distance travelled.
513 m
Distance is the area under the speed-time graph: triangle area = ½ × 3 × 38 = 57 m, plus rectangle area = 12 × 38 = 456 m. Total distance = 57 + 456 = 513 m.
9. On a speed-time graph, a train accelerates uniformly from rest to 16 m/s in 12 s and then continues at a constant speed of 16 m/s for a further 19 s. Calculate the total distance travelled.
400 m
Distance is the area under the speed-time graph: triangle area = ½ × 12 × 16 = 96 m, plus rectangle area = 19 × 16 = 304 m. Total distance = 96 + 304 = 400 m.
10. On a speed-time graph, a train accelerates uniformly from rest to 34 m/s in 10 s and then continues at a constant speed of 34 m/s for a further 16 s. Calculate the total distance travelled.
714 m
Distance is the area under the speed-time graph: triangle area = ½ × 10 × 34 = 170 m, plus rectangle area = 16 × 34 = 544 m. Total distance = 170 + 544 = 714 m.
11. On a speed-time graph, a train accelerates uniformly from rest to 32 m/s in 4 s and then continues at a constant speed of 32 m/s for a further 13 s. Calculate the total distance travelled.
480 m
Distance is the area under the speed-time graph: triangle area = ½ × 4 × 32 = 64 m, plus rectangle area = 13 × 32 = 416 m. Total distance = 64 + 416 = 480 m.
12. On a speed-time graph, a train accelerates uniformly from rest to 10 m/s in 2 s and then continues at a constant speed of 10 m/s for a further 9 s. Calculate the total distance travelled.
100 m
Distance is the area under the speed-time graph: triangle area = ½ × 2 × 10 = 10 m, plus rectangle area = 9 × 10 = 90 m. Total distance = 10 + 90 = 100 m.

12 questions · Seed 47 · Age guidance, not curriculum certification

Worksheet StudioPractice pack · Ages 13-15

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 2 s and then continues at a constant speed of 32 m/s for a further 10 s. Calculate the total distance travelled.
v_max = 32 m/s (t₁ = 2 s, t₂ = 10 s) · Distance = Area = ½vt₁ + vt₂
2. 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 7 s. Calculate the total distance travelled.
v_max = 46 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 46 m/s in 7 s and then continues at a constant speed of 46 m/s for a further 10 s. Calculate the total distance travelled.
v_max = 46 m/s (t₁ = 7 s, t₂ = 10 s) · Distance = Area = ½vt₁ + vt₂
4. On a speed-time graph, a train accelerates uniformly from rest to 22 m/s in 12 s and then continues at a constant speed of 22 m/s for a further 10 s. Calculate the total distance travelled.
v_max = 22 m/s (t₁ = 12 s, t₂ = 10 s) · Distance = Area = ½vt₁ + vt₂
5. On a speed-time graph, a train accelerates uniformly from rest to 44 m/s in 3 s and then continues at a constant speed of 44 m/s for a further 18 s. Calculate the total distance travelled.
v_max = 44 m/s (t₁ = 3 s, t₂ = 18 s) · Distance = Area = ½vt₁ + vt₂
6. On a speed-time graph, a train accelerates uniformly from rest to 20 m/s in 2 s and then continues at a constant speed of 20 m/s for a further 4 s. Calculate the total distance travelled.
v_max = 20 m/s (t₁ = 2 s, t₂ = 4 s) · Distance = Area = ½vt₁ + vt₂
7. On a speed-time graph, a train accelerates uniformly from rest to 30 m/s in 11 s and then continues at a constant speed of 30 m/s for a further 7 s. Calculate the total distance travelled.
v_max = 30 m/s (t₁ = 11 s, t₂ = 7 s) · Distance = Area = ½vt₁ + vt₂
8. On a speed-time graph, a train accelerates uniformly from rest to 38 m/s in 3 s and then continues at a constant speed of 38 m/s for a further 12 s. Calculate the total distance travelled.
v_max = 38 m/s (t₁ = 3 s, t₂ = 12 s) · Distance = Area = ½vt₁ + vt₂
9. On a speed-time graph, a train accelerates uniformly from rest to 16 m/s in 12 s and then continues at a constant speed of 16 m/s for a further 19 s. Calculate the total distance travelled.
v_max = 16 m/s (t₁ = 12 s, t₂ = 19 s) · Distance = Area = ½vt₁ + vt₂
10. On a speed-time graph, a train accelerates uniformly from rest to 34 m/s in 10 s and then continues at a constant speed of 34 m/s for a further 16 s. Calculate the total distance travelled.
v_max = 34 m/s (t₁ = 10 s, t₂ = 16 s) · Distance = Area = ½vt₁ + vt₂
11. On a speed-time graph, a train accelerates uniformly from rest to 32 m/s in 4 s and then continues at a constant speed of 32 m/s for a further 13 s. Calculate the total distance travelled.
v_max = 32 m/s (t₁ = 4 s, t₂ = 13 s) · Distance = Area = ½vt₁ + vt₂
12. On a speed-time graph, a train accelerates uniformly from rest to 10 m/s in 2 s and then continues at a constant speed of 10 m/s for a further 9 s. Calculate the total distance travelled.
v_max = 10 m/s (t₁ = 2 s, t₂ = 9 s) · Distance = Area = ½vt₁ + vt₂

12 questions · Seed 47 · Age guidance, not curriculum certification

Worksheet StudioAnswer key · Ages 13-15

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 2 s and then continues at a constant speed of 32 m/s for a further 10 s. Calculate the total distance travelled.
352 m
Distance is the area under the speed-time graph: triangle area = ½ × 2 × 32 = 32 m, plus rectangle area = 10 × 32 = 320 m. Total distance = 32 + 320 = 352 m.
2. 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 7 s. Calculate the total distance travelled.
391 m
Distance is the area under the speed-time graph: triangle area = ½ × 3 × 46 = 69 m, plus rectangle area = 7 × 46 = 322 m. Total distance = 69 + 322 = 391 m.
3. On a speed-time graph, a train accelerates uniformly from rest to 46 m/s in 7 s and then continues at a constant speed of 46 m/s for a further 10 s. Calculate the total distance travelled.
621 m
Distance is the area under the speed-time graph: triangle area = ½ × 7 × 46 = 161 m, plus rectangle area = 10 × 46 = 460 m. Total distance = 161 + 460 = 621 m.
4. On a speed-time graph, a train accelerates uniformly from rest to 22 m/s in 12 s and then continues at a constant speed of 22 m/s for a further 10 s. Calculate the total distance travelled.
352 m
Distance is the area under the speed-time graph: triangle area = ½ × 12 × 22 = 132 m, plus rectangle area = 10 × 22 = 220 m. Total distance = 132 + 220 = 352 m.
5. On a speed-time graph, a train accelerates uniformly from rest to 44 m/s in 3 s and then continues at a constant speed of 44 m/s for a further 18 s. Calculate the total distance travelled.
858 m
Distance is the area under the speed-time graph: triangle area = ½ × 3 × 44 = 66 m, plus rectangle area = 18 × 44 = 792 m. Total distance = 66 + 792 = 858 m.
6. On a speed-time graph, a train accelerates uniformly from rest to 20 m/s in 2 s and then continues at a constant speed of 20 m/s for a further 4 s. Calculate the total distance travelled.
100 m
Distance is the area under the speed-time graph: triangle area = ½ × 2 × 20 = 20 m, plus rectangle area = 4 × 20 = 80 m. Total distance = 20 + 80 = 100 m.
7. On a speed-time graph, a train accelerates uniformly from rest to 30 m/s in 11 s and then continues at a constant speed of 30 m/s for a further 7 s. Calculate the total distance travelled.
375 m
Distance is the area under the speed-time graph: triangle area = ½ × 11 × 30 = 165 m, plus rectangle area = 7 × 30 = 210 m. Total distance = 165 + 210 = 375 m.
8. On a speed-time graph, a train accelerates uniformly from rest to 38 m/s in 3 s and then continues at a constant speed of 38 m/s for a further 12 s. Calculate the total distance travelled.
513 m
Distance is the area under the speed-time graph: triangle area = ½ × 3 × 38 = 57 m, plus rectangle area = 12 × 38 = 456 m. Total distance = 57 + 456 = 513 m.
9. On a speed-time graph, a train accelerates uniformly from rest to 16 m/s in 12 s and then continues at a constant speed of 16 m/s for a further 19 s. Calculate the total distance travelled.
400 m
Distance is the area under the speed-time graph: triangle area = ½ × 12 × 16 = 96 m, plus rectangle area = 19 × 16 = 304 m. Total distance = 96 + 304 = 400 m.
10. On a speed-time graph, a train accelerates uniformly from rest to 34 m/s in 10 s and then continues at a constant speed of 34 m/s for a further 16 s. Calculate the total distance travelled.
714 m
Distance is the area under the speed-time graph: triangle area = ½ × 10 × 34 = 170 m, plus rectangle area = 16 × 34 = 544 m. Total distance = 170 + 544 = 714 m.
11. On a speed-time graph, a train accelerates uniformly from rest to 32 m/s in 4 s and then continues at a constant speed of 32 m/s for a further 13 s. Calculate the total distance travelled.
480 m
Distance is the area under the speed-time graph: triangle area = ½ × 4 × 32 = 64 m, plus rectangle area = 13 × 32 = 416 m. Total distance = 64 + 416 = 480 m.
12. On a speed-time graph, a train accelerates uniformly from rest to 10 m/s in 2 s and then continues at a constant speed of 10 m/s for a further 9 s. Calculate the total distance travelled.
100 m
Distance is the area under the speed-time graph: triangle area = ½ × 2 × 10 = 10 m, plus rectangle area = 9 × 10 = 90 m. Total distance = 10 + 90 = 100 m.

12 questions · Seed 47 · Age guidance, not curriculum certification