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.

New variation Try interactive challenge Browse templates

Age band:Ages 13-15 Ages 16-18

Choose “Save as PDF” to keep a copy. Use your browser’s paper setting for A4 or Letter.

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 10 m/s in 9 s and then continues at a constant speed of 10 m/s for a further 4 s. Calculate the total distance travelled.
v_max = 10 m/s (t₁ = 9 s, t₂ = 4 s) · Distance = Area = ½vt₁ + vt₂
2. On a speed-time graph, a train accelerates uniformly from rest to 42 m/s in 5 s and then continues at a constant speed of 42 m/s for a further 13 s. Calculate the total distance travelled.
v_max = 42 m/s (t₁ = 5 s, t₂ = 13 s) · Distance = Area = ½vt₁ + vt₂
3. On a speed-time graph, a train accelerates uniformly from rest to 22 m/s in 4 s and then continues at a constant speed of 22 m/s for a further 20 s. Calculate the total distance travelled.
v_max = 22 m/s (t₁ = 4 s, t₂ = 20 s) · Distance = Area = ½vt₁ + vt₂
4. On a speed-time graph, a train accelerates uniformly from rest to 34 m/s in 5 s and then continues at a constant speed of 34 m/s for a further 7 s. Calculate the total distance travelled.
v_max = 34 m/s (t₁ = 5 s, t₂ = 7 s) · Distance = Area = ½vt₁ + vt₂
5. On a speed-time graph, a train accelerates uniformly from rest to 42 m/s in 12 s and then continues at a constant speed of 42 m/s for a further 16 s. Calculate the total distance travelled.
v_max = 42 m/s (t₁ = 12 s, t₂ = 16 s) · Distance = Area = ½vt₁ + vt₂
6. On a speed-time graph, a train accelerates uniformly from rest to 30 m/s in 9 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 = 9 s, t₂ = 7 s) · Distance = Area = ½vt₁ + vt₂
7. On a speed-time graph, a train accelerates uniformly from rest to 46 m/s in 9 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 = 9 s, t₂ = 10 s) · Distance = Area = ½vt₁ + vt₂
8. On a speed-time graph, a train accelerates uniformly from rest to 12 m/s in 12 s and then continues at a constant speed of 12 m/s for a further 11 s. Calculate the total distance travelled.
v_max = 12 m/s (t₁ = 12 s, t₂ = 11 s) · Distance = Area = ½vt₁ + vt₂
9. 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 14 s. Calculate the total distance travelled.
v_max = 28 m/s (t₁ = 6 s, t₂ = 14 s) · Distance = Area = ½vt₁ + vt₂
10. On a speed-time graph, a train accelerates uniformly from rest to 8 m/s in 10 s and then continues at a constant speed of 8 m/s for a further 6 s. Calculate the total distance travelled.
v_max = 8 m/s (t₁ = 10 s, t₂ = 6 s) · Distance = Area = ½vt₁ + vt₂
11. 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 17 s. Calculate the total distance travelled.
v_max = 42 m/s (t₁ = 11 s, t₂ = 17 s) · Distance = Area = ½vt₁ + vt₂
12. On a speed-time graph, a train accelerates uniformly from rest to 26 m/s in 8 s and then continues at a constant speed of 26 m/s for a further 18 s. Calculate the total distance travelled.
v_max = 26 m/s (t₁ = 8 s, t₂ = 18 s) · Distance = Area = ½vt₁ + vt₂

12 questions · Seed 104735 · 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 10 m/s in 9 s and then continues at a constant speed of 10 m/s for a further 4 s. Calculate the total distance travelled.
85 m
Distance is the area under the speed-time graph: triangle area = ½ × 9 × 10 = 45 m, plus rectangle area = 4 × 10 = 40 m. Total distance = 45 + 40 = 85 m.
2. On a speed-time graph, a train accelerates uniformly from rest to 42 m/s in 5 s and then continues at a constant speed of 42 m/s for a further 13 s. Calculate the total distance travelled.
651 m
Distance is the area under the speed-time graph: triangle area = ½ × 5 × 42 = 105 m, plus rectangle area = 13 × 42 = 546 m. Total distance = 105 + 546 = 651 m.
3. On a speed-time graph, a train accelerates uniformly from rest to 22 m/s in 4 s and then continues at a constant speed of 22 m/s for a further 20 s. Calculate the total distance travelled.
484 m
Distance is the area under the speed-time graph: triangle area = ½ × 4 × 22 = 44 m, plus rectangle area = 20 × 22 = 440 m. Total distance = 44 + 440 = 484 m.
4. On a speed-time graph, a train accelerates uniformly from rest to 34 m/s in 5 s and then continues at a constant speed of 34 m/s for a further 7 s. Calculate the total distance travelled.
323 m
Distance is the area under the speed-time graph: triangle area = ½ × 5 × 34 = 85 m, plus rectangle area = 7 × 34 = 238 m. Total distance = 85 + 238 = 323 m.
5. On a speed-time graph, a train accelerates uniformly from rest to 42 m/s in 12 s and then continues at a constant speed of 42 m/s for a further 16 s. Calculate the total distance travelled.
924 m
Distance is the area under the speed-time graph: triangle area = ½ × 12 × 42 = 252 m, plus rectangle area = 16 × 42 = 672 m. Total distance = 252 + 672 = 924 m.
6. On a speed-time graph, a train accelerates uniformly from rest to 30 m/s in 9 s and then continues at a constant speed of 30 m/s for a further 7 s. Calculate the total distance travelled.
345 m
Distance is the area under the speed-time graph: triangle area = ½ × 9 × 30 = 135 m, plus rectangle area = 7 × 30 = 210 m. Total distance = 135 + 210 = 345 m.
7. On a speed-time graph, a train accelerates uniformly from rest to 46 m/s in 9 s and then continues at a constant speed of 46 m/s for a further 10 s. Calculate the total distance travelled.
667 m
Distance is the area under the speed-time graph: triangle area = ½ × 9 × 46 = 207 m, plus rectangle area = 10 × 46 = 460 m. Total distance = 207 + 460 = 667 m.
8. On a speed-time graph, a train accelerates uniformly from rest to 12 m/s in 12 s and then continues at a constant speed of 12 m/s for a further 11 s. Calculate the total distance travelled.
204 m
Distance is the area under the speed-time graph: triangle area = ½ × 12 × 12 = 72 m, plus rectangle area = 11 × 12 = 132 m. Total distance = 72 + 132 = 204 m.
9. 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 14 s. Calculate the total distance travelled.
476 m
Distance is the area under the speed-time graph: triangle area = ½ × 6 × 28 = 84 m, plus rectangle area = 14 × 28 = 392 m. Total distance = 84 + 392 = 476 m.
10. On a speed-time graph, a train accelerates uniformly from rest to 8 m/s in 10 s and then continues at a constant speed of 8 m/s for a further 6 s. Calculate the total distance travelled.
88 m
Distance is the area under the speed-time graph: triangle area = ½ × 10 × 8 = 40 m, plus rectangle area = 6 × 8 = 48 m. Total distance = 40 + 48 = 88 m.
11. 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 17 s. Calculate the total distance travelled.
945 m
Distance is the area under the speed-time graph: triangle area = ½ × 11 × 42 = 231 m, plus rectangle area = 17 × 42 = 714 m. Total distance = 231 + 714 = 945 m.
12. On a speed-time graph, a train accelerates uniformly from rest to 26 m/s in 8 s and then continues at a constant speed of 26 m/s for a further 18 s. Calculate the total distance travelled.
572 m
Distance is the area under the speed-time graph: triangle area = ½ × 8 × 26 = 104 m, plus rectangle area = 18 × 26 = 468 m. Total distance = 104 + 468 = 572 m.

12 questions · Seed 104735 · 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 10 m/s in 9 s and then continues at a constant speed of 10 m/s for a further 4 s. Calculate the total distance travelled.
v_max = 10 m/s (t₁ = 9 s, t₂ = 4 s) · Distance = Area = ½vt₁ + vt₂
2. On a speed-time graph, a train accelerates uniformly from rest to 42 m/s in 5 s and then continues at a constant speed of 42 m/s for a further 13 s. Calculate the total distance travelled.
v_max = 42 m/s (t₁ = 5 s, t₂ = 13 s) · Distance = Area = ½vt₁ + vt₂
3. On a speed-time graph, a train accelerates uniformly from rest to 22 m/s in 4 s and then continues at a constant speed of 22 m/s for a further 20 s. Calculate the total distance travelled.
v_max = 22 m/s (t₁ = 4 s, t₂ = 20 s) · Distance = Area = ½vt₁ + vt₂
4. On a speed-time graph, a train accelerates uniformly from rest to 34 m/s in 5 s and then continues at a constant speed of 34 m/s for a further 7 s. Calculate the total distance travelled.
v_max = 34 m/s (t₁ = 5 s, t₂ = 7 s) · Distance = Area = ½vt₁ + vt₂
5. On a speed-time graph, a train accelerates uniformly from rest to 42 m/s in 12 s and then continues at a constant speed of 42 m/s for a further 16 s. Calculate the total distance travelled.
v_max = 42 m/s (t₁ = 12 s, t₂ = 16 s) · Distance = Area = ½vt₁ + vt₂
6. On a speed-time graph, a train accelerates uniformly from rest to 30 m/s in 9 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 = 9 s, t₂ = 7 s) · Distance = Area = ½vt₁ + vt₂
7. On a speed-time graph, a train accelerates uniformly from rest to 46 m/s in 9 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 = 9 s, t₂ = 10 s) · Distance = Area = ½vt₁ + vt₂
8. On a speed-time graph, a train accelerates uniformly from rest to 12 m/s in 12 s and then continues at a constant speed of 12 m/s for a further 11 s. Calculate the total distance travelled.
v_max = 12 m/s (t₁ = 12 s, t₂ = 11 s) · Distance = Area = ½vt₁ + vt₂
9. 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 14 s. Calculate the total distance travelled.
v_max = 28 m/s (t₁ = 6 s, t₂ = 14 s) · Distance = Area = ½vt₁ + vt₂
10. On a speed-time graph, a train accelerates uniformly from rest to 8 m/s in 10 s and then continues at a constant speed of 8 m/s for a further 6 s. Calculate the total distance travelled.
v_max = 8 m/s (t₁ = 10 s, t₂ = 6 s) · Distance = Area = ½vt₁ + vt₂
11. 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 17 s. Calculate the total distance travelled.
v_max = 42 m/s (t₁ = 11 s, t₂ = 17 s) · Distance = Area = ½vt₁ + vt₂
12. On a speed-time graph, a train accelerates uniformly from rest to 26 m/s in 8 s and then continues at a constant speed of 26 m/s for a further 18 s. Calculate the total distance travelled.
v_max = 26 m/s (t₁ = 8 s, t₂ = 18 s) · Distance = Area = ½vt₁ + vt₂

12 questions · Seed 104735 · 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 10 m/s in 9 s and then continues at a constant speed of 10 m/s for a further 4 s. Calculate the total distance travelled.
85 m
Distance is the area under the speed-time graph: triangle area = ½ × 9 × 10 = 45 m, plus rectangle area = 4 × 10 = 40 m. Total distance = 45 + 40 = 85 m.
2. On a speed-time graph, a train accelerates uniformly from rest to 42 m/s in 5 s and then continues at a constant speed of 42 m/s for a further 13 s. Calculate the total distance travelled.
651 m
Distance is the area under the speed-time graph: triangle area = ½ × 5 × 42 = 105 m, plus rectangle area = 13 × 42 = 546 m. Total distance = 105 + 546 = 651 m.
3. On a speed-time graph, a train accelerates uniformly from rest to 22 m/s in 4 s and then continues at a constant speed of 22 m/s for a further 20 s. Calculate the total distance travelled.
484 m
Distance is the area under the speed-time graph: triangle area = ½ × 4 × 22 = 44 m, plus rectangle area = 20 × 22 = 440 m. Total distance = 44 + 440 = 484 m.
4. On a speed-time graph, a train accelerates uniformly from rest to 34 m/s in 5 s and then continues at a constant speed of 34 m/s for a further 7 s. Calculate the total distance travelled.
323 m
Distance is the area under the speed-time graph: triangle area = ½ × 5 × 34 = 85 m, plus rectangle area = 7 × 34 = 238 m. Total distance = 85 + 238 = 323 m.
5. On a speed-time graph, a train accelerates uniformly from rest to 42 m/s in 12 s and then continues at a constant speed of 42 m/s for a further 16 s. Calculate the total distance travelled.
924 m
Distance is the area under the speed-time graph: triangle area = ½ × 12 × 42 = 252 m, plus rectangle area = 16 × 42 = 672 m. Total distance = 252 + 672 = 924 m.
6. On a speed-time graph, a train accelerates uniformly from rest to 30 m/s in 9 s and then continues at a constant speed of 30 m/s for a further 7 s. Calculate the total distance travelled.
345 m
Distance is the area under the speed-time graph: triangle area = ½ × 9 × 30 = 135 m, plus rectangle area = 7 × 30 = 210 m. Total distance = 135 + 210 = 345 m.
7. On a speed-time graph, a train accelerates uniformly from rest to 46 m/s in 9 s and then continues at a constant speed of 46 m/s for a further 10 s. Calculate the total distance travelled.
667 m
Distance is the area under the speed-time graph: triangle area = ½ × 9 × 46 = 207 m, plus rectangle area = 10 × 46 = 460 m. Total distance = 207 + 460 = 667 m.
8. On a speed-time graph, a train accelerates uniformly from rest to 12 m/s in 12 s and then continues at a constant speed of 12 m/s for a further 11 s. Calculate the total distance travelled.
204 m
Distance is the area under the speed-time graph: triangle area = ½ × 12 × 12 = 72 m, plus rectangle area = 11 × 12 = 132 m. Total distance = 72 + 132 = 204 m.
9. 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 14 s. Calculate the total distance travelled.
476 m
Distance is the area under the speed-time graph: triangle area = ½ × 6 × 28 = 84 m, plus rectangle area = 14 × 28 = 392 m. Total distance = 84 + 392 = 476 m.
10. On a speed-time graph, a train accelerates uniformly from rest to 8 m/s in 10 s and then continues at a constant speed of 8 m/s for a further 6 s. Calculate the total distance travelled.
88 m
Distance is the area under the speed-time graph: triangle area = ½ × 10 × 8 = 40 m, plus rectangle area = 6 × 8 = 48 m. Total distance = 40 + 48 = 88 m.
11. 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 17 s. Calculate the total distance travelled.
945 m
Distance is the area under the speed-time graph: triangle area = ½ × 11 × 42 = 231 m, plus rectangle area = 17 × 42 = 714 m. Total distance = 231 + 714 = 945 m.
12. On a speed-time graph, a train accelerates uniformly from rest to 26 m/s in 8 s and then continues at a constant speed of 26 m/s for a further 18 s. Calculate the total distance travelled.
572 m
Distance is the area under the speed-time graph: triangle area = ½ × 8 × 26 = 104 m, plus rectangle area = 18 × 26 = 468 m. Total distance = 104 + 468 = 572 m.

12 questions · Seed 104735 · Age guidance, not curriculum certification