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 36 m/s in 8 s and then continues at a constant speed of 36 m/s for a further 13 s. Calculate the total distance travelled.
v_max = 36 m/s (t₁ = 8 s, t₂ = 13 s) · Distance = Area = ½vt₁ + vt₂
2. On a speed-time graph, a train accelerates uniformly from rest to 16 m/s in 2 s and then continues at a constant speed of 16 m/s for a further 9 s. Calculate the total distance travelled.
v_max = 16 m/s (t₁ = 2 s, t₂ = 9 s) · Distance = Area = ½vt₁ + vt₂
3. On a speed-time graph, a train accelerates uniformly from rest to 28 m/s in 3 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 = 3 s, t₂ = 17 s) · Distance = Area = ½vt₁ + vt₂
4. On a speed-time graph, a train accelerates uniformly from rest to 8 m/s in 11 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 = 11 s, t₂ = 7 s) · Distance = Area = ½vt₁ + vt₂
5. On a speed-time graph, a train accelerates uniformly from rest to 48 m/s in 5 s and then continues at a constant speed of 48 m/s for a further 8 s. Calculate the total distance travelled.
v_max = 48 m/s (t₁ = 5 s, t₂ = 8 s) · Distance = Area = ½vt₁ + vt₂
6. On a speed-time graph, a train accelerates uniformly from rest to 42 m/s in 9 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 = 9 s, t₂ = 10 s) · Distance = Area = ½vt₁ + vt₂
7. On a speed-time graph, a train accelerates uniformly from rest to 42 m/s in 11 s and then continues at a constant speed of 42 m/s for a further 20 s. Calculate the total distance travelled.
v_max = 42 m/s (t₁ = 11 s, t₂ = 20 s) · Distance = Area = ½vt₁ + vt₂
8. On a speed-time graph, a train accelerates uniformly from rest to 28 m/s in 7 s and then continues at a constant speed of 28 m/s for a further 12 s. Calculate the total distance travelled.
v_max = 28 m/s (t₁ = 7 s, t₂ = 12 s) · Distance = Area = ½vt₁ + vt₂
9. On a speed-time graph, a train accelerates uniformly from rest to 26 m/s in 9 s and then continues at a constant speed of 26 m/s for a further 10 s. Calculate the total distance travelled.
v_max = 26 m/s (t₁ = 9 s, t₂ = 10 s) · Distance = Area = ½vt₁ + vt₂
10. 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 4 s. Calculate the total distance travelled.
v_max = 38 m/s (t₁ = 7 s, t₂ = 4 s) · Distance = Area = ½vt₁ + vt₂
11. On a speed-time graph, a train accelerates uniformly from rest to 8 m/s in 11 s and then continues at a constant speed of 8 m/s for a further 8 s. Calculate the total distance travelled.
v_max = 8 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 18 m/s in 7 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 = 7 s, t₂ = 18 s) · Distance = Area = ½vt₁ + vt₂

12 questions · Seed 42 · 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 36 m/s in 8 s and then continues at a constant speed of 36 m/s for a further 13 s. Calculate the total distance travelled.
612 m
Distance is the area under the speed-time graph: triangle area = ½ × 8 × 36 = 144 m, plus rectangle area = 13 × 36 = 468 m. Total distance = 144 + 468 = 612 m.
2. On a speed-time graph, a train accelerates uniformly from rest to 16 m/s in 2 s and then continues at a constant speed of 16 m/s for a further 9 s. Calculate the total distance travelled.
160 m
Distance is the area under the speed-time graph: triangle area = ½ × 2 × 16 = 16 m, plus rectangle area = 9 × 16 = 144 m. Total distance = 16 + 144 = 160 m.
3. On a speed-time graph, a train accelerates uniformly from rest to 28 m/s in 3 s and then continues at a constant speed of 28 m/s for a further 17 s. Calculate the total distance travelled.
518 m
Distance is the area under the speed-time graph: triangle area = ½ × 3 × 28 = 42 m, plus rectangle area = 17 × 28 = 476 m. Total distance = 42 + 476 = 518 m.
4. On a speed-time graph, a train accelerates uniformly from rest to 8 m/s in 11 s and then continues at a constant speed of 8 m/s for a further 7 s. Calculate the total distance travelled.
100 m
Distance is the area under the speed-time graph: triangle area = ½ × 11 × 8 = 44 m, plus rectangle area = 7 × 8 = 56 m. Total distance = 44 + 56 = 100 m.
5. On a speed-time graph, a train accelerates uniformly from rest to 48 m/s in 5 s and then continues at a constant speed of 48 m/s for a further 8 s. Calculate the total distance travelled.
504 m
Distance is the area under the speed-time graph: triangle area = ½ × 5 × 48 = 120 m, plus rectangle area = 8 × 48 = 384 m. Total distance = 120 + 384 = 504 m.
6. On a speed-time graph, a train accelerates uniformly from rest to 42 m/s in 9 s and then continues at a constant speed of 42 m/s for a further 10 s. Calculate the total distance travelled.
609 m
Distance is the area under the speed-time graph: triangle area = ½ × 9 × 42 = 189 m, plus rectangle area = 10 × 42 = 420 m. Total distance = 189 + 420 = 609 m.
7. On a speed-time graph, a train accelerates uniformly from rest to 42 m/s in 11 s and then continues at a constant speed of 42 m/s for a further 20 s. Calculate the total distance travelled.
1071 m
Distance is the area under the speed-time graph: triangle area = ½ × 11 × 42 = 231 m, plus rectangle area = 20 × 42 = 840 m. Total distance = 231 + 840 = 1071 m.
8. On a speed-time graph, a train accelerates uniformly from rest to 28 m/s in 7 s and then continues at a constant speed of 28 m/s for a further 12 s. Calculate the total distance travelled.
434 m
Distance is the area under the speed-time graph: triangle area = ½ × 7 × 28 = 98 m, plus rectangle area = 12 × 28 = 336 m. Total distance = 98 + 336 = 434 m.
9. On a speed-time graph, a train accelerates uniformly from rest to 26 m/s in 9 s and then continues at a constant speed of 26 m/s for a further 10 s. Calculate the total distance travelled.
377 m
Distance is the area under the speed-time graph: triangle area = ½ × 9 × 26 = 117 m, plus rectangle area = 10 × 26 = 260 m. Total distance = 117 + 260 = 377 m.
10. 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 4 s. Calculate the total distance travelled.
285 m
Distance is the area under the speed-time graph: triangle area = ½ × 7 × 38 = 133 m, plus rectangle area = 4 × 38 = 152 m. Total distance = 133 + 152 = 285 m.
11. On a speed-time graph, a train accelerates uniformly from rest to 8 m/s in 11 s and then continues at a constant speed of 8 m/s for a further 8 s. Calculate the total distance travelled.
108 m
Distance is the area under the speed-time graph: triangle area = ½ × 11 × 8 = 44 m, plus rectangle area = 8 × 8 = 64 m. Total distance = 44 + 64 = 108 m.
12. On a speed-time graph, a train accelerates uniformly from rest to 18 m/s in 7 s and then continues at a constant speed of 18 m/s for a further 18 s. Calculate the total distance travelled.
387 m
Distance is the area under the speed-time graph: triangle area = ½ × 7 × 18 = 63 m, plus rectangle area = 18 × 18 = 324 m. Total distance = 63 + 324 = 387 m.

12 questions · Seed 42 · 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 36 m/s in 8 s and then continues at a constant speed of 36 m/s for a further 13 s. Calculate the total distance travelled.
v_max = 36 m/s (t₁ = 8 s, t₂ = 13 s) · Distance = Area = ½vt₁ + vt₂
2. On a speed-time graph, a train accelerates uniformly from rest to 16 m/s in 2 s and then continues at a constant speed of 16 m/s for a further 9 s. Calculate the total distance travelled.
v_max = 16 m/s (t₁ = 2 s, t₂ = 9 s) · Distance = Area = ½vt₁ + vt₂
3. On a speed-time graph, a train accelerates uniformly from rest to 28 m/s in 3 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 = 3 s, t₂ = 17 s) · Distance = Area = ½vt₁ + vt₂
4. On a speed-time graph, a train accelerates uniformly from rest to 8 m/s in 11 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 = 11 s, t₂ = 7 s) · Distance = Area = ½vt₁ + vt₂
5. On a speed-time graph, a train accelerates uniformly from rest to 48 m/s in 5 s and then continues at a constant speed of 48 m/s for a further 8 s. Calculate the total distance travelled.
v_max = 48 m/s (t₁ = 5 s, t₂ = 8 s) · Distance = Area = ½vt₁ + vt₂
6. On a speed-time graph, a train accelerates uniformly from rest to 42 m/s in 9 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 = 9 s, t₂ = 10 s) · Distance = Area = ½vt₁ + vt₂
7. On a speed-time graph, a train accelerates uniformly from rest to 42 m/s in 11 s and then continues at a constant speed of 42 m/s for a further 20 s. Calculate the total distance travelled.
v_max = 42 m/s (t₁ = 11 s, t₂ = 20 s) · Distance = Area = ½vt₁ + vt₂
8. On a speed-time graph, a train accelerates uniformly from rest to 28 m/s in 7 s and then continues at a constant speed of 28 m/s for a further 12 s. Calculate the total distance travelled.
v_max = 28 m/s (t₁ = 7 s, t₂ = 12 s) · Distance = Area = ½vt₁ + vt₂
9. On a speed-time graph, a train accelerates uniformly from rest to 26 m/s in 9 s and then continues at a constant speed of 26 m/s for a further 10 s. Calculate the total distance travelled.
v_max = 26 m/s (t₁ = 9 s, t₂ = 10 s) · Distance = Area = ½vt₁ + vt₂
10. 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 4 s. Calculate the total distance travelled.
v_max = 38 m/s (t₁ = 7 s, t₂ = 4 s) · Distance = Area = ½vt₁ + vt₂
11. On a speed-time graph, a train accelerates uniformly from rest to 8 m/s in 11 s and then continues at a constant speed of 8 m/s for a further 8 s. Calculate the total distance travelled.
v_max = 8 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 18 m/s in 7 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 = 7 s, t₂ = 18 s) · Distance = Area = ½vt₁ + vt₂

12 questions · Seed 42 · 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 36 m/s in 8 s and then continues at a constant speed of 36 m/s for a further 13 s. Calculate the total distance travelled.
612 m
Distance is the area under the speed-time graph: triangle area = ½ × 8 × 36 = 144 m, plus rectangle area = 13 × 36 = 468 m. Total distance = 144 + 468 = 612 m.
2. On a speed-time graph, a train accelerates uniformly from rest to 16 m/s in 2 s and then continues at a constant speed of 16 m/s for a further 9 s. Calculate the total distance travelled.
160 m
Distance is the area under the speed-time graph: triangle area = ½ × 2 × 16 = 16 m, plus rectangle area = 9 × 16 = 144 m. Total distance = 16 + 144 = 160 m.
3. On a speed-time graph, a train accelerates uniformly from rest to 28 m/s in 3 s and then continues at a constant speed of 28 m/s for a further 17 s. Calculate the total distance travelled.
518 m
Distance is the area under the speed-time graph: triangle area = ½ × 3 × 28 = 42 m, plus rectangle area = 17 × 28 = 476 m. Total distance = 42 + 476 = 518 m.
4. On a speed-time graph, a train accelerates uniformly from rest to 8 m/s in 11 s and then continues at a constant speed of 8 m/s for a further 7 s. Calculate the total distance travelled.
100 m
Distance is the area under the speed-time graph: triangle area = ½ × 11 × 8 = 44 m, plus rectangle area = 7 × 8 = 56 m. Total distance = 44 + 56 = 100 m.
5. On a speed-time graph, a train accelerates uniformly from rest to 48 m/s in 5 s and then continues at a constant speed of 48 m/s for a further 8 s. Calculate the total distance travelled.
504 m
Distance is the area under the speed-time graph: triangle area = ½ × 5 × 48 = 120 m, plus rectangle area = 8 × 48 = 384 m. Total distance = 120 + 384 = 504 m.
6. On a speed-time graph, a train accelerates uniformly from rest to 42 m/s in 9 s and then continues at a constant speed of 42 m/s for a further 10 s. Calculate the total distance travelled.
609 m
Distance is the area under the speed-time graph: triangle area = ½ × 9 × 42 = 189 m, plus rectangle area = 10 × 42 = 420 m. Total distance = 189 + 420 = 609 m.
7. On a speed-time graph, a train accelerates uniformly from rest to 42 m/s in 11 s and then continues at a constant speed of 42 m/s for a further 20 s. Calculate the total distance travelled.
1071 m
Distance is the area under the speed-time graph: triangle area = ½ × 11 × 42 = 231 m, plus rectangle area = 20 × 42 = 840 m. Total distance = 231 + 840 = 1071 m.
8. On a speed-time graph, a train accelerates uniformly from rest to 28 m/s in 7 s and then continues at a constant speed of 28 m/s for a further 12 s. Calculate the total distance travelled.
434 m
Distance is the area under the speed-time graph: triangle area = ½ × 7 × 28 = 98 m, plus rectangle area = 12 × 28 = 336 m. Total distance = 98 + 336 = 434 m.
9. On a speed-time graph, a train accelerates uniformly from rest to 26 m/s in 9 s and then continues at a constant speed of 26 m/s for a further 10 s. Calculate the total distance travelled.
377 m
Distance is the area under the speed-time graph: triangle area = ½ × 9 × 26 = 117 m, plus rectangle area = 10 × 26 = 260 m. Total distance = 117 + 260 = 377 m.
10. 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 4 s. Calculate the total distance travelled.
285 m
Distance is the area under the speed-time graph: triangle area = ½ × 7 × 38 = 133 m, plus rectangle area = 4 × 38 = 152 m. Total distance = 133 + 152 = 285 m.
11. On a speed-time graph, a train accelerates uniformly from rest to 8 m/s in 11 s and then continues at a constant speed of 8 m/s for a further 8 s. Calculate the total distance travelled.
108 m
Distance is the area under the speed-time graph: triangle area = ½ × 11 × 8 = 44 m, plus rectangle area = 8 × 8 = 64 m. Total distance = 44 + 64 = 108 m.
12. On a speed-time graph, a train accelerates uniformly from rest to 18 m/s in 7 s and then continues at a constant speed of 18 m/s for a further 18 s. Calculate the total distance travelled.
387 m
Distance is the area under the speed-time graph: triangle area = ½ × 7 × 18 = 63 m, plus rectangle area = 18 × 18 = 324 m. Total distance = 63 + 324 = 387 m.

12 questions · Seed 42 · Age guidance, not curriculum certification