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 42 m/s in 2 s and then continues at a constant speed of 42 m/s for a further 19 s. Calculate the total distance travelled.
v_max = 42 m/s (t₁ = 2 s, t₂ = 19 s) · Distance = Area = ½vt₁ + vt₂
2. On a speed-time graph, a train accelerates uniformly from rest to 14 m/s in 7 s and then continues at a constant speed of 14 m/s for a further 6 s. Calculate the total distance travelled.
v_max = 14 m/s (t₁ = 7 s, t₂ = 6 s) · Distance = Area = ½vt₁ + vt₂
3. On a speed-time graph, a train accelerates uniformly from rest to 32 m/s in 10 s and then continues at a constant speed of 32 m/s for a further 9 s. Calculate the total distance travelled.
v_max = 32 m/s (t₁ = 10 s, t₂ = 9 s) · Distance = Area = ½vt₁ + vt₂
4. On a speed-time graph, a train accelerates uniformly from rest to 22 m/s in 3 s and then continues at a constant speed of 22 m/s for a further 9 s. Calculate the total distance travelled.
v_max = 22 m/s (t₁ = 3 s, t₂ = 9 s) · Distance = Area = ½vt₁ + vt₂
5. On a speed-time graph, a train accelerates uniformly from rest to 32 m/s in 12 s and then continues at a constant speed of 32 m/s for a further 11 s. Calculate the total distance travelled.
v_max = 32 m/s (t₁ = 12 s, t₂ = 11 s) · Distance = Area = ½vt₁ + vt₂
6. On a speed-time graph, a train accelerates uniformly from rest to 18 m/s in 2 s and then continues at a constant speed of 18 m/s for a further 5 s. Calculate the total distance travelled.
v_max = 18 m/s (t₁ = 2 s, t₂ = 5 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 9 s. Calculate the total distance travelled.
v_max = 22 m/s (t₁ = 6 s, t₂ = 9 s) · Distance = Area = ½vt₁ + vt₂
8. On a speed-time graph, a train accelerates uniformly from rest to 44 m/s in 2 s and then continues at a constant speed of 44 m/s for a further 13 s. Calculate the total distance travelled.
v_max = 44 m/s (t₁ = 2 s, t₂ = 13 s) · Distance = Area = ½vt₁ + vt₂
9. On a speed-time graph, a train accelerates uniformly from rest to 28 m/s in 11 s and then continues at a constant speed of 28 m/s for a further 9 s. Calculate the total distance travelled.
v_max = 28 m/s (t₁ = 11 s, t₂ = 9 s) · Distance = Area = ½vt₁ + vt₂
10. On a speed-time graph, a train accelerates uniformly from rest to 24 m/s in 6 s and then continues at a constant speed of 24 m/s for a further 9 s. Calculate the total distance travelled.
v_max = 24 m/s (t₁ = 6 s, t₂ = 9 s) · Distance = Area = ½vt₁ + vt₂
11. On a speed-time graph, a train accelerates uniformly from rest to 34 m/s in 8 s and then continues at a constant speed of 34 m/s for a further 15 s. Calculate the total distance travelled.
v_max = 34 m/s (t₁ = 8 s, t₂ = 15 s) · Distance = Area = ½vt₁ + vt₂
12. 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

12 questions · Seed 104732 · Age guidance, not curriculum certification

View the answer key

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 42 m/s in 2 s and then continues at a constant speed of 42 m/s for a further 19 s. Calculate the total distance travelled.
840 m
Distance is the area under the speed-time graph: triangle area = ½ × 2 × 42 = 42 m, plus rectangle area = 19 × 42 = 798 m. Total distance = 42 + 798 = 840 m.
2. On a speed-time graph, a train accelerates uniformly from rest to 14 m/s in 7 s and then continues at a constant speed of 14 m/s for a further 6 s. Calculate the total distance travelled.
133 m
Distance is the area under the speed-time graph: triangle area = ½ × 7 × 14 = 49 m, plus rectangle area = 6 × 14 = 84 m. Total distance = 49 + 84 = 133 m.
3. On a speed-time graph, a train accelerates uniformly from rest to 32 m/s in 10 s and then continues at a constant speed of 32 m/s for a further 9 s. Calculate the total distance travelled.
448 m
Distance is the area under the speed-time graph: triangle area = ½ × 10 × 32 = 160 m, plus rectangle area = 9 × 32 = 288 m. Total distance = 160 + 288 = 448 m.
4. On a speed-time graph, a train accelerates uniformly from rest to 22 m/s in 3 s and then continues at a constant speed of 22 m/s for a further 9 s. Calculate the total distance travelled.
231 m
Distance is the area under the speed-time graph: triangle area = ½ × 3 × 22 = 33 m, plus rectangle area = 9 × 22 = 198 m. Total distance = 33 + 198 = 231 m.
5. On a speed-time graph, a train accelerates uniformly from rest to 32 m/s in 12 s and then continues at a constant speed of 32 m/s for a further 11 s. Calculate the total distance travelled.
544 m
Distance is the area under the speed-time graph: triangle area = ½ × 12 × 32 = 192 m, plus rectangle area = 11 × 32 = 352 m. Total distance = 192 + 352 = 544 m.
6. On a speed-time graph, a train accelerates uniformly from rest to 18 m/s in 2 s and then continues at a constant speed of 18 m/s for a further 5 s. Calculate the total distance travelled.
108 m
Distance is the area under the speed-time graph: triangle area = ½ × 2 × 18 = 18 m, plus rectangle area = 5 × 18 = 90 m. Total distance = 18 + 90 = 108 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 9 s. Calculate the total distance travelled.
264 m
Distance is the area under the speed-time graph: triangle area = ½ × 6 × 22 = 66 m, plus rectangle area = 9 × 22 = 198 m. Total distance = 66 + 198 = 264 m.
8. On a speed-time graph, a train accelerates uniformly from rest to 44 m/s in 2 s and then continues at a constant speed of 44 m/s for a further 13 s. Calculate the total distance travelled.
616 m
Distance is the area under the speed-time graph: triangle area = ½ × 2 × 44 = 44 m, plus rectangle area = 13 × 44 = 572 m. Total distance = 44 + 572 = 616 m.
9. On a speed-time graph, a train accelerates uniformly from rest to 28 m/s in 11 s and then continues at a constant speed of 28 m/s for a further 9 s. Calculate the total distance travelled.
406 m
Distance is the area under the speed-time graph: triangle area = ½ × 11 × 28 = 154 m, plus rectangle area = 9 × 28 = 252 m. Total distance = 154 + 252 = 406 m.
10. On a speed-time graph, a train accelerates uniformly from rest to 24 m/s in 6 s and then continues at a constant speed of 24 m/s for a further 9 s. Calculate the total distance travelled.
288 m
Distance is the area under the speed-time graph: triangle area = ½ × 6 × 24 = 72 m, plus rectangle area = 9 × 24 = 216 m. Total distance = 72 + 216 = 288 m.
11. On a speed-time graph, a train accelerates uniformly from rest to 34 m/s in 8 s and then continues at a constant speed of 34 m/s for a further 15 s. Calculate the total distance travelled.
646 m
Distance is the area under the speed-time graph: triangle area = ½ × 8 × 34 = 136 m, plus rectangle area = 15 × 34 = 510 m. Total distance = 136 + 510 = 646 m.
12. 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.

12 questions · Seed 104732 · 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 42 m/s in 2 s and then continues at a constant speed of 42 m/s for a further 19 s. Calculate the total distance travelled.
v_max = 42 m/s (t₁ = 2 s, t₂ = 19 s) · Distance = Area = ½vt₁ + vt₂
2. On a speed-time graph, a train accelerates uniformly from rest to 14 m/s in 7 s and then continues at a constant speed of 14 m/s for a further 6 s. Calculate the total distance travelled.
v_max = 14 m/s (t₁ = 7 s, t₂ = 6 s) · Distance = Area = ½vt₁ + vt₂
3. On a speed-time graph, a train accelerates uniformly from rest to 32 m/s in 10 s and then continues at a constant speed of 32 m/s for a further 9 s. Calculate the total distance travelled.
v_max = 32 m/s (t₁ = 10 s, t₂ = 9 s) · Distance = Area = ½vt₁ + vt₂
4. On a speed-time graph, a train accelerates uniformly from rest to 22 m/s in 3 s and then continues at a constant speed of 22 m/s for a further 9 s. Calculate the total distance travelled.
v_max = 22 m/s (t₁ = 3 s, t₂ = 9 s) · Distance = Area = ½vt₁ + vt₂
5. On a speed-time graph, a train accelerates uniformly from rest to 32 m/s in 12 s and then continues at a constant speed of 32 m/s for a further 11 s. Calculate the total distance travelled.
v_max = 32 m/s (t₁ = 12 s, t₂ = 11 s) · Distance = Area = ½vt₁ + vt₂
6. On a speed-time graph, a train accelerates uniformly from rest to 18 m/s in 2 s and then continues at a constant speed of 18 m/s for a further 5 s. Calculate the total distance travelled.
v_max = 18 m/s (t₁ = 2 s, t₂ = 5 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 9 s. Calculate the total distance travelled.
v_max = 22 m/s (t₁ = 6 s, t₂ = 9 s) · Distance = Area = ½vt₁ + vt₂
8. On a speed-time graph, a train accelerates uniformly from rest to 44 m/s in 2 s and then continues at a constant speed of 44 m/s for a further 13 s. Calculate the total distance travelled.
v_max = 44 m/s (t₁ = 2 s, t₂ = 13 s) · Distance = Area = ½vt₁ + vt₂
9. On a speed-time graph, a train accelerates uniformly from rest to 28 m/s in 11 s and then continues at a constant speed of 28 m/s for a further 9 s. Calculate the total distance travelled.
v_max = 28 m/s (t₁ = 11 s, t₂ = 9 s) · Distance = Area = ½vt₁ + vt₂
10. On a speed-time graph, a train accelerates uniformly from rest to 24 m/s in 6 s and then continues at a constant speed of 24 m/s for a further 9 s. Calculate the total distance travelled.
v_max = 24 m/s (t₁ = 6 s, t₂ = 9 s) · Distance = Area = ½vt₁ + vt₂
11. On a speed-time graph, a train accelerates uniformly from rest to 34 m/s in 8 s and then continues at a constant speed of 34 m/s for a further 15 s. Calculate the total distance travelled.
v_max = 34 m/s (t₁ = 8 s, t₂ = 15 s) · Distance = Area = ½vt₁ + vt₂
12. 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

12 questions · Seed 104732 · 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 42 m/s in 2 s and then continues at a constant speed of 42 m/s for a further 19 s. Calculate the total distance travelled.
840 m
Distance is the area under the speed-time graph: triangle area = ½ × 2 × 42 = 42 m, plus rectangle area = 19 × 42 = 798 m. Total distance = 42 + 798 = 840 m.
2. On a speed-time graph, a train accelerates uniformly from rest to 14 m/s in 7 s and then continues at a constant speed of 14 m/s for a further 6 s. Calculate the total distance travelled.
133 m
Distance is the area under the speed-time graph: triangle area = ½ × 7 × 14 = 49 m, plus rectangle area = 6 × 14 = 84 m. Total distance = 49 + 84 = 133 m.
3. On a speed-time graph, a train accelerates uniformly from rest to 32 m/s in 10 s and then continues at a constant speed of 32 m/s for a further 9 s. Calculate the total distance travelled.
448 m
Distance is the area under the speed-time graph: triangle area = ½ × 10 × 32 = 160 m, plus rectangle area = 9 × 32 = 288 m. Total distance = 160 + 288 = 448 m.
4. On a speed-time graph, a train accelerates uniformly from rest to 22 m/s in 3 s and then continues at a constant speed of 22 m/s for a further 9 s. Calculate the total distance travelled.
231 m
Distance is the area under the speed-time graph: triangle area = ½ × 3 × 22 = 33 m, plus rectangle area = 9 × 22 = 198 m. Total distance = 33 + 198 = 231 m.
5. On a speed-time graph, a train accelerates uniformly from rest to 32 m/s in 12 s and then continues at a constant speed of 32 m/s for a further 11 s. Calculate the total distance travelled.
544 m
Distance is the area under the speed-time graph: triangle area = ½ × 12 × 32 = 192 m, plus rectangle area = 11 × 32 = 352 m. Total distance = 192 + 352 = 544 m.
6. On a speed-time graph, a train accelerates uniformly from rest to 18 m/s in 2 s and then continues at a constant speed of 18 m/s for a further 5 s. Calculate the total distance travelled.
108 m
Distance is the area under the speed-time graph: triangle area = ½ × 2 × 18 = 18 m, plus rectangle area = 5 × 18 = 90 m. Total distance = 18 + 90 = 108 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 9 s. Calculate the total distance travelled.
264 m
Distance is the area under the speed-time graph: triangle area = ½ × 6 × 22 = 66 m, plus rectangle area = 9 × 22 = 198 m. Total distance = 66 + 198 = 264 m.
8. On a speed-time graph, a train accelerates uniformly from rest to 44 m/s in 2 s and then continues at a constant speed of 44 m/s for a further 13 s. Calculate the total distance travelled.
616 m
Distance is the area under the speed-time graph: triangle area = ½ × 2 × 44 = 44 m, plus rectangle area = 13 × 44 = 572 m. Total distance = 44 + 572 = 616 m.
9. On a speed-time graph, a train accelerates uniformly from rest to 28 m/s in 11 s and then continues at a constant speed of 28 m/s for a further 9 s. Calculate the total distance travelled.
406 m
Distance is the area under the speed-time graph: triangle area = ½ × 11 × 28 = 154 m, plus rectangle area = 9 × 28 = 252 m. Total distance = 154 + 252 = 406 m.
10. On a speed-time graph, a train accelerates uniformly from rest to 24 m/s in 6 s and then continues at a constant speed of 24 m/s for a further 9 s. Calculate the total distance travelled.
288 m
Distance is the area under the speed-time graph: triangle area = ½ × 6 × 24 = 72 m, plus rectangle area = 9 × 24 = 216 m. Total distance = 72 + 216 = 288 m.
11. On a speed-time graph, a train accelerates uniformly from rest to 34 m/s in 8 s and then continues at a constant speed of 34 m/s for a further 15 s. Calculate the total distance travelled.
646 m
Distance is the area under the speed-time graph: triangle area = ½ × 8 × 34 = 136 m, plus rectangle area = 15 × 34 = 510 m. Total distance = 136 + 510 = 646 m.
12. 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.

12 questions · Seed 104732 · Age guidance, not curriculum certification