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 12 m/s in 8 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 = 8 s, t₂ = 15 s) · Distance = Area = ½vt₁ + vt₂
2. On a speed-time graph, a train accelerates uniformly from rest to 38 m/s in 7 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 = 7 s, t₂ = 12 s) · Distance = Area = ½vt₁ + vt₂
3. 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 15 s. Calculate the total distance travelled.
v_max = 32 m/s (t₁ = 2 s, t₂ = 15 s) · Distance = Area = ½vt₁ + vt₂
4. 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 17 s. Calculate the total distance travelled.
v_max = 28 m/s (t₁ = 6 s, t₂ = 17 s) · Distance = Area = ½vt₁ + vt₂
5. On a speed-time graph, a train accelerates uniformly from rest to 30 m/s in 3 s and then continues at a constant speed of 30 m/s for a further 5 s. Calculate the total distance travelled.
v_max = 30 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 42 m/s in 6 s and then continues at a constant speed of 42 m/s for a further 10 s. Calculate the total distance travelled.
v_max = 42 m/s (t₁ = 6 s, t₂ = 10 s) · Distance = Area = ½vt₁ + vt₂
7. On a speed-time graph, a train accelerates uniformly from rest to 8 m/s in 6 s and then continues at a constant speed of 8 m/s for a further 4 s. Calculate the total distance travelled.
v_max = 8 m/s (t₁ = 6 s, t₂ = 4 s) · Distance = Area = ½vt₁ + vt₂
8. On a speed-time graph, a train accelerates uniformly from rest to 50 m/s in 7 s and then continues at a constant speed of 50 m/s for a further 5 s. Calculate the total distance travelled.
v_max = 50 m/s (t₁ = 7 s, t₂ = 5 s) · Distance = Area = ½vt₁ + vt₂
9. On a speed-time graph, a train accelerates uniformly from rest to 18 m/s in 9 s and then continues at a constant speed of 18 m/s for a further 18 s. Calculate the total distance travelled.
v_max = 18 m/s (t₁ = 9 s, t₂ = 18 s) · Distance = Area = ½vt₁ + vt₂
10. 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 17 s. Calculate the total distance travelled.
v_max = 38 m/s (t₁ = 3 s, t₂ = 17 s) · Distance = Area = ½vt₁ + vt₂
11. On a speed-time graph, a train accelerates uniformly from rest to 14 m/s in 6 s and then continues at a constant speed of 14 m/s for a further 10 s. Calculate the total distance travelled.
v_max = 14 m/s (t₁ = 6 s, t₂ = 10 s) · Distance = Area = ½vt₁ + vt₂
12. On a speed-time graph, a train accelerates uniformly from rest to 28 m/s in 8 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 = 8 s, t₂ = 10 s) · Distance = Area = ½vt₁ + vt₂

12 questions · Seed 54 · 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 12 m/s in 8 s and then continues at a constant speed of 12 m/s for a further 15 s. Calculate the total distance travelled.
228 m
Distance is the area under the speed-time graph: triangle area = ½ × 8 × 12 = 48 m, plus rectangle area = 15 × 12 = 180 m. Total distance = 48 + 180 = 228 m.
2. On a speed-time graph, a train accelerates uniformly from rest to 38 m/s in 7 s and then continues at a constant speed of 38 m/s for a further 12 s. Calculate the total distance travelled.
589 m
Distance is the area under the speed-time graph: triangle area = ½ × 7 × 38 = 133 m, plus rectangle area = 12 × 38 = 456 m. Total distance = 133 + 456 = 589 m.
3. 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 15 s. Calculate the total distance travelled.
512 m
Distance is the area under the speed-time graph: triangle area = ½ × 2 × 32 = 32 m, plus rectangle area = 15 × 32 = 480 m. Total distance = 32 + 480 = 512 m.
4. 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 17 s. Calculate the total distance travelled.
560 m
Distance is the area under the speed-time graph: triangle area = ½ × 6 × 28 = 84 m, plus rectangle area = 17 × 28 = 476 m. Total distance = 84 + 476 = 560 m.
5. On a speed-time graph, a train accelerates uniformly from rest to 30 m/s in 3 s and then continues at a constant speed of 30 m/s for a further 5 s. Calculate the total distance travelled.
195 m
Distance is the area under the speed-time graph: triangle area = ½ × 3 × 30 = 45 m, plus rectangle area = 5 × 30 = 150 m. Total distance = 45 + 150 = 195 m.
6. On a speed-time graph, a train accelerates uniformly from rest to 42 m/s in 6 s and then continues at a constant speed of 42 m/s for a further 10 s. Calculate the total distance travelled.
546 m
Distance is the area under the speed-time graph: triangle area = ½ × 6 × 42 = 126 m, plus rectangle area = 10 × 42 = 420 m. Total distance = 126 + 420 = 546 m.
7. On a speed-time graph, a train accelerates uniformly from rest to 8 m/s in 6 s and then continues at a constant speed of 8 m/s for a further 4 s. Calculate the total distance travelled.
56 m
Distance is the area under the speed-time graph: triangle area = ½ × 6 × 8 = 24 m, plus rectangle area = 4 × 8 = 32 m. Total distance = 24 + 32 = 56 m.
8. On a speed-time graph, a train accelerates uniformly from rest to 50 m/s in 7 s and then continues at a constant speed of 50 m/s for a further 5 s. Calculate the total distance travelled.
425 m
Distance is the area under the speed-time graph: triangle area = ½ × 7 × 50 = 175 m, plus rectangle area = 5 × 50 = 250 m. Total distance = 175 + 250 = 425 m.
9. On a speed-time graph, a train accelerates uniformly from rest to 18 m/s in 9 s and then continues at a constant speed of 18 m/s for a further 18 s. Calculate the total distance travelled.
405 m
Distance is the area under the speed-time graph: triangle area = ½ × 9 × 18 = 81 m, plus rectangle area = 18 × 18 = 324 m. Total distance = 81 + 324 = 405 m.
10. 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 17 s. Calculate the total distance travelled.
703 m
Distance is the area under the speed-time graph: triangle area = ½ × 3 × 38 = 57 m, plus rectangle area = 17 × 38 = 646 m. Total distance = 57 + 646 = 703 m.
11. On a speed-time graph, a train accelerates uniformly from rest to 14 m/s in 6 s and then continues at a constant speed of 14 m/s for a further 10 s. Calculate the total distance travelled.
182 m
Distance is the area under the speed-time graph: triangle area = ½ × 6 × 14 = 42 m, plus rectangle area = 10 × 14 = 140 m. Total distance = 42 + 140 = 182 m.
12. On a speed-time graph, a train accelerates uniformly from rest to 28 m/s in 8 s and then continues at a constant speed of 28 m/s for a further 10 s. Calculate the total distance travelled.
392 m
Distance is the area under the speed-time graph: triangle area = ½ × 8 × 28 = 112 m, plus rectangle area = 10 × 28 = 280 m. Total distance = 112 + 280 = 392 m.

12 questions · Seed 54 · 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 12 m/s in 8 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 = 8 s, t₂ = 15 s) · Distance = Area = ½vt₁ + vt₂
2. On a speed-time graph, a train accelerates uniformly from rest to 38 m/s in 7 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 = 7 s, t₂ = 12 s) · Distance = Area = ½vt₁ + vt₂
3. 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 15 s. Calculate the total distance travelled.
v_max = 32 m/s (t₁ = 2 s, t₂ = 15 s) · Distance = Area = ½vt₁ + vt₂
4. 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 17 s. Calculate the total distance travelled.
v_max = 28 m/s (t₁ = 6 s, t₂ = 17 s) · Distance = Area = ½vt₁ + vt₂
5. On a speed-time graph, a train accelerates uniformly from rest to 30 m/s in 3 s and then continues at a constant speed of 30 m/s for a further 5 s. Calculate the total distance travelled.
v_max = 30 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 42 m/s in 6 s and then continues at a constant speed of 42 m/s for a further 10 s. Calculate the total distance travelled.
v_max = 42 m/s (t₁ = 6 s, t₂ = 10 s) · Distance = Area = ½vt₁ + vt₂
7. On a speed-time graph, a train accelerates uniformly from rest to 8 m/s in 6 s and then continues at a constant speed of 8 m/s for a further 4 s. Calculate the total distance travelled.
v_max = 8 m/s (t₁ = 6 s, t₂ = 4 s) · Distance = Area = ½vt₁ + vt₂
8. On a speed-time graph, a train accelerates uniformly from rest to 50 m/s in 7 s and then continues at a constant speed of 50 m/s for a further 5 s. Calculate the total distance travelled.
v_max = 50 m/s (t₁ = 7 s, t₂ = 5 s) · Distance = Area = ½vt₁ + vt₂
9. On a speed-time graph, a train accelerates uniformly from rest to 18 m/s in 9 s and then continues at a constant speed of 18 m/s for a further 18 s. Calculate the total distance travelled.
v_max = 18 m/s (t₁ = 9 s, t₂ = 18 s) · Distance = Area = ½vt₁ + vt₂
10. 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 17 s. Calculate the total distance travelled.
v_max = 38 m/s (t₁ = 3 s, t₂ = 17 s) · Distance = Area = ½vt₁ + vt₂
11. On a speed-time graph, a train accelerates uniformly from rest to 14 m/s in 6 s and then continues at a constant speed of 14 m/s for a further 10 s. Calculate the total distance travelled.
v_max = 14 m/s (t₁ = 6 s, t₂ = 10 s) · Distance = Area = ½vt₁ + vt₂
12. On a speed-time graph, a train accelerates uniformly from rest to 28 m/s in 8 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 = 8 s, t₂ = 10 s) · Distance = Area = ½vt₁ + vt₂

12 questions · Seed 54 · 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 12 m/s in 8 s and then continues at a constant speed of 12 m/s for a further 15 s. Calculate the total distance travelled.
228 m
Distance is the area under the speed-time graph: triangle area = ½ × 8 × 12 = 48 m, plus rectangle area = 15 × 12 = 180 m. Total distance = 48 + 180 = 228 m.
2. On a speed-time graph, a train accelerates uniformly from rest to 38 m/s in 7 s and then continues at a constant speed of 38 m/s for a further 12 s. Calculate the total distance travelled.
589 m
Distance is the area under the speed-time graph: triangle area = ½ × 7 × 38 = 133 m, plus rectangle area = 12 × 38 = 456 m. Total distance = 133 + 456 = 589 m.
3. 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 15 s. Calculate the total distance travelled.
512 m
Distance is the area under the speed-time graph: triangle area = ½ × 2 × 32 = 32 m, plus rectangle area = 15 × 32 = 480 m. Total distance = 32 + 480 = 512 m.
4. 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 17 s. Calculate the total distance travelled.
560 m
Distance is the area under the speed-time graph: triangle area = ½ × 6 × 28 = 84 m, plus rectangle area = 17 × 28 = 476 m. Total distance = 84 + 476 = 560 m.
5. On a speed-time graph, a train accelerates uniformly from rest to 30 m/s in 3 s and then continues at a constant speed of 30 m/s for a further 5 s. Calculate the total distance travelled.
195 m
Distance is the area under the speed-time graph: triangle area = ½ × 3 × 30 = 45 m, plus rectangle area = 5 × 30 = 150 m. Total distance = 45 + 150 = 195 m.
6. On a speed-time graph, a train accelerates uniformly from rest to 42 m/s in 6 s and then continues at a constant speed of 42 m/s for a further 10 s. Calculate the total distance travelled.
546 m
Distance is the area under the speed-time graph: triangle area = ½ × 6 × 42 = 126 m, plus rectangle area = 10 × 42 = 420 m. Total distance = 126 + 420 = 546 m.
7. On a speed-time graph, a train accelerates uniformly from rest to 8 m/s in 6 s and then continues at a constant speed of 8 m/s for a further 4 s. Calculate the total distance travelled.
56 m
Distance is the area under the speed-time graph: triangle area = ½ × 6 × 8 = 24 m, plus rectangle area = 4 × 8 = 32 m. Total distance = 24 + 32 = 56 m.
8. On a speed-time graph, a train accelerates uniformly from rest to 50 m/s in 7 s and then continues at a constant speed of 50 m/s for a further 5 s. Calculate the total distance travelled.
425 m
Distance is the area under the speed-time graph: triangle area = ½ × 7 × 50 = 175 m, plus rectangle area = 5 × 50 = 250 m. Total distance = 175 + 250 = 425 m.
9. On a speed-time graph, a train accelerates uniformly from rest to 18 m/s in 9 s and then continues at a constant speed of 18 m/s for a further 18 s. Calculate the total distance travelled.
405 m
Distance is the area under the speed-time graph: triangle area = ½ × 9 × 18 = 81 m, plus rectangle area = 18 × 18 = 324 m. Total distance = 81 + 324 = 405 m.
10. 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 17 s. Calculate the total distance travelled.
703 m
Distance is the area under the speed-time graph: triangle area = ½ × 3 × 38 = 57 m, plus rectangle area = 17 × 38 = 646 m. Total distance = 57 + 646 = 703 m.
11. On a speed-time graph, a train accelerates uniformly from rest to 14 m/s in 6 s and then continues at a constant speed of 14 m/s for a further 10 s. Calculate the total distance travelled.
182 m
Distance is the area under the speed-time graph: triangle area = ½ × 6 × 14 = 42 m, plus rectangle area = 10 × 14 = 140 m. Total distance = 42 + 140 = 182 m.
12. On a speed-time graph, a train accelerates uniformly from rest to 28 m/s in 8 s and then continues at a constant speed of 28 m/s for a further 10 s. Calculate the total distance travelled.
392 m
Distance is the area under the speed-time graph: triangle area = ½ × 8 × 28 = 112 m, plus rectangle area = 10 × 28 = 280 m. Total distance = 112 + 280 = 392 m.

12 questions · Seed 54 · Age guidance, not curriculum certification