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 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
2. 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 11 s. Calculate the total distance travelled.
v_max = 34 m/s (t₁ = 8 s, t₂ = 11 s) · Distance = Area = ½vt₁ + vt₂
3. On a speed-time graph, a train accelerates uniformly from rest to 40 m/s in 5 s and then continues at a constant speed of 40 m/s for a further 20 s. Calculate the total distance travelled.
v_max = 40 m/s (t₁ = 5 s, t₂ = 20 s) · Distance = Area = ½vt₁ + vt₂
4. 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
5. On a speed-time graph, a train accelerates uniformly from rest to 12 m/s in 3 s and then continues at a constant speed of 12 m/s for a further 5 s. Calculate the total distance travelled.
v_max = 12 m/s (t₁ = 3 s, t₂ = 5 s) · Distance = Area = ½vt₁ + vt₂
6. 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 17 s. Calculate the total distance travelled.
v_max = 44 m/s (t₁ = 3 s, t₂ = 17 s) · Distance = Area = ½vt₁ + vt₂
7. On a speed-time graph, a train accelerates uniformly from rest to 26 m/s in 11 s and then continues at a constant speed of 26 m/s for a further 7 s. Calculate the total distance travelled.
v_max = 26 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 12 m/s in 4 s and then continues at a constant speed of 12 m/s for a further 15 s. Calculate the total distance travelled.
v_max = 12 m/s (t₁ = 4 s, t₂ = 15 s) · Distance = Area = ½vt₁ + vt₂
9. On a speed-time graph, a train accelerates uniformly from rest to 22 m/s in 7 s and then continues at a constant speed of 22 m/s for a further 4 s. Calculate the total distance travelled.
v_max = 22 m/s (t₁ = 7 s, t₂ = 4 s) · Distance = Area = ½vt₁ + vt₂
10. On a speed-time graph, a train accelerates uniformly from rest to 48 m/s in 6 s and then continues at a constant speed of 48 m/s for a further 7 s. Calculate the total distance travelled.
v_max = 48 m/s (t₁ = 6 s, t₂ = 7 s) · Distance = Area = ½vt₁ + vt₂
11. On a speed-time graph, a train accelerates uniformly from rest to 26 m/s in 11 s and then continues at a constant speed of 26 m/s for a further 8 s. Calculate the total distance travelled.
v_max = 26 m/s (t₁ = 11 s, t₂ = 8 s) · Distance = Area = ½vt₁ + vt₂
12. On a speed-time graph, a train accelerates uniformly from rest to 28 m/s in 10 s and then continues at a constant speed of 28 m/s for a further 10 s. Calculate the total distance travelled.
v_max = 28 m/s (t₁ = 10 s, t₂ = 10 s) · Distance = Area = ½vt₁ + vt₂

12 questions · Seed 104729 · 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 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.
2. 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 11 s. Calculate the total distance travelled.
510 m
Distance is the area under the speed-time graph: triangle area = ½ × 8 × 34 = 136 m, plus rectangle area = 11 × 34 = 374 m. Total distance = 136 + 374 = 510 m.
3. On a speed-time graph, a train accelerates uniformly from rest to 40 m/s in 5 s and then continues at a constant speed of 40 m/s for a further 20 s. Calculate the total distance travelled.
900 m
Distance is the area under the speed-time graph: triangle area = ½ × 5 × 40 = 100 m, plus rectangle area = 20 × 40 = 800 m. Total distance = 100 + 800 = 900 m.
4. 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.
5. On a speed-time graph, a train accelerates uniformly from rest to 12 m/s in 3 s and then continues at a constant speed of 12 m/s for a further 5 s. Calculate the total distance travelled.
78 m
Distance is the area under the speed-time graph: triangle area = ½ × 3 × 12 = 18 m, plus rectangle area = 5 × 12 = 60 m. Total distance = 18 + 60 = 78 m.
6. 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 17 s. Calculate the total distance travelled.
814 m
Distance is the area under the speed-time graph: triangle area = ½ × 3 × 44 = 66 m, plus rectangle area = 17 × 44 = 748 m. Total distance = 66 + 748 = 814 m.
7. On a speed-time graph, a train accelerates uniformly from rest to 26 m/s in 11 s and then continues at a constant speed of 26 m/s for a further 7 s. Calculate the total distance travelled.
325 m
Distance is the area under the speed-time graph: triangle area = ½ × 11 × 26 = 143 m, plus rectangle area = 7 × 26 = 182 m. Total distance = 143 + 182 = 325 m.
8. On a speed-time graph, a train accelerates uniformly from rest to 12 m/s in 4 s and then continues at a constant speed of 12 m/s for a further 15 s. Calculate the total distance travelled.
204 m
Distance is the area under the speed-time graph: triangle area = ½ × 4 × 12 = 24 m, plus rectangle area = 15 × 12 = 180 m. Total distance = 24 + 180 = 204 m.
9. On a speed-time graph, a train accelerates uniformly from rest to 22 m/s in 7 s and then continues at a constant speed of 22 m/s for a further 4 s. Calculate the total distance travelled.
165 m
Distance is the area under the speed-time graph: triangle area = ½ × 7 × 22 = 77 m, plus rectangle area = 4 × 22 = 88 m. Total distance = 77 + 88 = 165 m.
10. On a speed-time graph, a train accelerates uniformly from rest to 48 m/s in 6 s and then continues at a constant speed of 48 m/s for a further 7 s. Calculate the total distance travelled.
480 m
Distance is the area under the speed-time graph: triangle area = ½ × 6 × 48 = 144 m, plus rectangle area = 7 × 48 = 336 m. Total distance = 144 + 336 = 480 m.
11. On a speed-time graph, a train accelerates uniformly from rest to 26 m/s in 11 s and then continues at a constant speed of 26 m/s for a further 8 s. Calculate the total distance travelled.
351 m
Distance is the area under the speed-time graph: triangle area = ½ × 11 × 26 = 143 m, plus rectangle area = 8 × 26 = 208 m. Total distance = 143 + 208 = 351 m.
12. On a speed-time graph, a train accelerates uniformly from rest to 28 m/s in 10 s and then continues at a constant speed of 28 m/s for a further 10 s. Calculate the total distance travelled.
420 m
Distance is the area under the speed-time graph: triangle area = ½ × 10 × 28 = 140 m, plus rectangle area = 10 × 28 = 280 m. Total distance = 140 + 280 = 420 m.

12 questions · Seed 104729 · 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 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
2. 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 11 s. Calculate the total distance travelled.
v_max = 34 m/s (t₁ = 8 s, t₂ = 11 s) · Distance = Area = ½vt₁ + vt₂
3. On a speed-time graph, a train accelerates uniformly from rest to 40 m/s in 5 s and then continues at a constant speed of 40 m/s for a further 20 s. Calculate the total distance travelled.
v_max = 40 m/s (t₁ = 5 s, t₂ = 20 s) · Distance = Area = ½vt₁ + vt₂
4. 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
5. On a speed-time graph, a train accelerates uniformly from rest to 12 m/s in 3 s and then continues at a constant speed of 12 m/s for a further 5 s. Calculate the total distance travelled.
v_max = 12 m/s (t₁ = 3 s, t₂ = 5 s) · Distance = Area = ½vt₁ + vt₂
6. 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 17 s. Calculate the total distance travelled.
v_max = 44 m/s (t₁ = 3 s, t₂ = 17 s) · Distance = Area = ½vt₁ + vt₂
7. On a speed-time graph, a train accelerates uniformly from rest to 26 m/s in 11 s and then continues at a constant speed of 26 m/s for a further 7 s. Calculate the total distance travelled.
v_max = 26 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 12 m/s in 4 s and then continues at a constant speed of 12 m/s for a further 15 s. Calculate the total distance travelled.
v_max = 12 m/s (t₁ = 4 s, t₂ = 15 s) · Distance = Area = ½vt₁ + vt₂
9. On a speed-time graph, a train accelerates uniformly from rest to 22 m/s in 7 s and then continues at a constant speed of 22 m/s for a further 4 s. Calculate the total distance travelled.
v_max = 22 m/s (t₁ = 7 s, t₂ = 4 s) · Distance = Area = ½vt₁ + vt₂
10. On a speed-time graph, a train accelerates uniformly from rest to 48 m/s in 6 s and then continues at a constant speed of 48 m/s for a further 7 s. Calculate the total distance travelled.
v_max = 48 m/s (t₁ = 6 s, t₂ = 7 s) · Distance = Area = ½vt₁ + vt₂
11. On a speed-time graph, a train accelerates uniformly from rest to 26 m/s in 11 s and then continues at a constant speed of 26 m/s for a further 8 s. Calculate the total distance travelled.
v_max = 26 m/s (t₁ = 11 s, t₂ = 8 s) · Distance = Area = ½vt₁ + vt₂
12. On a speed-time graph, a train accelerates uniformly from rest to 28 m/s in 10 s and then continues at a constant speed of 28 m/s for a further 10 s. Calculate the total distance travelled.
v_max = 28 m/s (t₁ = 10 s, t₂ = 10 s) · Distance = Area = ½vt₁ + vt₂

12 questions · Seed 104729 · 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 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.
2. 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 11 s. Calculate the total distance travelled.
510 m
Distance is the area under the speed-time graph: triangle area = ½ × 8 × 34 = 136 m, plus rectangle area = 11 × 34 = 374 m. Total distance = 136 + 374 = 510 m.
3. On a speed-time graph, a train accelerates uniformly from rest to 40 m/s in 5 s and then continues at a constant speed of 40 m/s for a further 20 s. Calculate the total distance travelled.
900 m
Distance is the area under the speed-time graph: triangle area = ½ × 5 × 40 = 100 m, plus rectangle area = 20 × 40 = 800 m. Total distance = 100 + 800 = 900 m.
4. 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.
5. On a speed-time graph, a train accelerates uniformly from rest to 12 m/s in 3 s and then continues at a constant speed of 12 m/s for a further 5 s. Calculate the total distance travelled.
78 m
Distance is the area under the speed-time graph: triangle area = ½ × 3 × 12 = 18 m, plus rectangle area = 5 × 12 = 60 m. Total distance = 18 + 60 = 78 m.
6. 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 17 s. Calculate the total distance travelled.
814 m
Distance is the area under the speed-time graph: triangle area = ½ × 3 × 44 = 66 m, plus rectangle area = 17 × 44 = 748 m. Total distance = 66 + 748 = 814 m.
7. On a speed-time graph, a train accelerates uniformly from rest to 26 m/s in 11 s and then continues at a constant speed of 26 m/s for a further 7 s. Calculate the total distance travelled.
325 m
Distance is the area under the speed-time graph: triangle area = ½ × 11 × 26 = 143 m, plus rectangle area = 7 × 26 = 182 m. Total distance = 143 + 182 = 325 m.
8. On a speed-time graph, a train accelerates uniformly from rest to 12 m/s in 4 s and then continues at a constant speed of 12 m/s for a further 15 s. Calculate the total distance travelled.
204 m
Distance is the area under the speed-time graph: triangle area = ½ × 4 × 12 = 24 m, plus rectangle area = 15 × 12 = 180 m. Total distance = 24 + 180 = 204 m.
9. On a speed-time graph, a train accelerates uniformly from rest to 22 m/s in 7 s and then continues at a constant speed of 22 m/s for a further 4 s. Calculate the total distance travelled.
165 m
Distance is the area under the speed-time graph: triangle area = ½ × 7 × 22 = 77 m, plus rectangle area = 4 × 22 = 88 m. Total distance = 77 + 88 = 165 m.
10. On a speed-time graph, a train accelerates uniformly from rest to 48 m/s in 6 s and then continues at a constant speed of 48 m/s for a further 7 s. Calculate the total distance travelled.
480 m
Distance is the area under the speed-time graph: triangle area = ½ × 6 × 48 = 144 m, plus rectangle area = 7 × 48 = 336 m. Total distance = 144 + 336 = 480 m.
11. On a speed-time graph, a train accelerates uniformly from rest to 26 m/s in 11 s and then continues at a constant speed of 26 m/s for a further 8 s. Calculate the total distance travelled.
351 m
Distance is the area under the speed-time graph: triangle area = ½ × 11 × 26 = 143 m, plus rectangle area = 8 × 26 = 208 m. Total distance = 143 + 208 = 351 m.
12. On a speed-time graph, a train accelerates uniformly from rest to 28 m/s in 10 s and then continues at a constant speed of 28 m/s for a further 10 s. Calculate the total distance travelled.
420 m
Distance is the area under the speed-time graph: triangle area = ½ × 10 × 28 = 140 m, plus rectangle area = 10 × 28 = 280 m. Total distance = 140 + 280 = 420 m.

12 questions · Seed 104729 · Age guidance, not curriculum certification