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 42 m/s in 10 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 = 10 s, t₂ = 13 s) · Distance = Area = ½vt₁ + vt₂
2. On a speed-time graph, a train accelerates uniformly from rest to 12 m/s in 2 s and then continues at a constant speed of 12 m/s for a further 19 s. Calculate the total distance travelled.
v_max = 12 m/s (t₁ = 2 s, t₂ = 19 s) · Distance = Area = ½vt₁ + vt₂
3. 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 15 s. Calculate the total distance travelled.
v_max = 46 m/s (t₁ = 9 s, t₂ = 15 s) · Distance = Area = ½vt₁ + vt₂
4. On a speed-time graph, a train accelerates uniformly from rest to 16 m/s in 4 s and then continues at a constant speed of 16 m/s for a further 13 s. Calculate the total distance travelled.
v_max = 16 m/s (t₁ = 4 s, t₂ = 13 s) · Distance = Area = ½vt₁ + vt₂
5. On a speed-time graph, a train accelerates uniformly from rest to 46 m/s in 5 s and then continues at a constant speed of 46 m/s for a further 4 s. Calculate the total distance travelled.
v_max = 46 m/s (t₁ = 5 s, t₂ = 4 s) · Distance = Area = ½vt₁ + vt₂
6. On a speed-time graph, a train accelerates uniformly from rest to 22 m/s in 10 s and then continues at a constant speed of 22 m/s for a further 10 s. Calculate the total distance travelled.
v_max = 22 m/s (t₁ = 10 s, t₂ = 10 s) · Distance = Area = ½vt₁ + vt₂
7. 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 12 s. Calculate the total distance travelled.
v_max = 22 m/s (t₁ = 3 s, t₂ = 12 s) · Distance = Area = ½vt₁ + vt₂
8. On a speed-time graph, a train accelerates uniformly from rest to 50 m/s in 3 s and then continues at a constant speed of 50 m/s for a further 20 s. Calculate the total distance travelled.
v_max = 50 m/s (t₁ = 3 s, t₂ = 20 s) · Distance = Area = ½vt₁ + vt₂
9. On a speed-time graph, a train accelerates uniformly from rest to 40 m/s in 6 s and then continues at a constant speed of 40 m/s for a further 13 s. Calculate the total distance travelled.
v_max = 40 m/s (t₁ = 6 s, t₂ = 13 s) · Distance = Area = ½vt₁ + vt₂
10. 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 16 s. Calculate the total distance travelled.
v_max = 12 m/s (t₁ = 4 s, t₂ = 16 s) · Distance = Area = ½vt₁ + vt₂
11. On a speed-time graph, a train accelerates uniformly from rest to 26 m/s in 4 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 = 4 s, t₂ = 18 s) · Distance = Area = ½vt₁ + vt₂
12. On a speed-time graph, a train accelerates uniformly from rest to 48 m/s in 11 s and then continues at a constant speed of 48 m/s for a further 5 s. Calculate the total distance travelled.
v_max = 48 m/s (t₁ = 11 s, t₂ = 5 s) · Distance = Area = ½vt₁ + vt₂

12 questions · Seed 46 · Age guidance, not curriculum certification

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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 42 m/s in 10 s and then continues at a constant speed of 42 m/s for a further 13 s. Calculate the total distance travelled.
756 m
Distance is the area under the speed-time graph: triangle area = ½ × 10 × 42 = 210 m, plus rectangle area = 13 × 42 = 546 m. Total distance = 210 + 546 = 756 m.
2. On a speed-time graph, a train accelerates uniformly from rest to 12 m/s in 2 s and then continues at a constant speed of 12 m/s for a further 19 s. Calculate the total distance travelled.
240 m
Distance is the area under the speed-time graph: triangle area = ½ × 2 × 12 = 12 m, plus rectangle area = 19 × 12 = 228 m. Total distance = 12 + 228 = 240 m.
3. 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 15 s. Calculate the total distance travelled.
897 m
Distance is the area under the speed-time graph: triangle area = ½ × 9 × 46 = 207 m, plus rectangle area = 15 × 46 = 690 m. Total distance = 207 + 690 = 897 m.
4. On a speed-time graph, a train accelerates uniformly from rest to 16 m/s in 4 s and then continues at a constant speed of 16 m/s for a further 13 s. Calculate the total distance travelled.
240 m
Distance is the area under the speed-time graph: triangle area = ½ × 4 × 16 = 32 m, plus rectangle area = 13 × 16 = 208 m. Total distance = 32 + 208 = 240 m.
5. On a speed-time graph, a train accelerates uniformly from rest to 46 m/s in 5 s and then continues at a constant speed of 46 m/s for a further 4 s. Calculate the total distance travelled.
299 m
Distance is the area under the speed-time graph: triangle area = ½ × 5 × 46 = 115 m, plus rectangle area = 4 × 46 = 184 m. Total distance = 115 + 184 = 299 m.
6. On a speed-time graph, a train accelerates uniformly from rest to 22 m/s in 10 s and then continues at a constant speed of 22 m/s for a further 10 s. Calculate the total distance travelled.
330 m
Distance is the area under the speed-time graph: triangle area = ½ × 10 × 22 = 110 m, plus rectangle area = 10 × 22 = 220 m. Total distance = 110 + 220 = 330 m.
7. 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 12 s. Calculate the total distance travelled.
297 m
Distance is the area under the speed-time graph: triangle area = ½ × 3 × 22 = 33 m, plus rectangle area = 12 × 22 = 264 m. Total distance = 33 + 264 = 297 m.
8. On a speed-time graph, a train accelerates uniformly from rest to 50 m/s in 3 s and then continues at a constant speed of 50 m/s for a further 20 s. Calculate the total distance travelled.
1075 m
Distance is the area under the speed-time graph: triangle area = ½ × 3 × 50 = 75 m, plus rectangle area = 20 × 50 = 1000 m. Total distance = 75 + 1000 = 1075 m.
9. On a speed-time graph, a train accelerates uniformly from rest to 40 m/s in 6 s and then continues at a constant speed of 40 m/s for a further 13 s. Calculate the total distance travelled.
640 m
Distance is the area under the speed-time graph: triangle area = ½ × 6 × 40 = 120 m, plus rectangle area = 13 × 40 = 520 m. Total distance = 120 + 520 = 640 m.
10. 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 16 s. Calculate the total distance travelled.
216 m
Distance is the area under the speed-time graph: triangle area = ½ × 4 × 12 = 24 m, plus rectangle area = 16 × 12 = 192 m. Total distance = 24 + 192 = 216 m.
11. On a speed-time graph, a train accelerates uniformly from rest to 26 m/s in 4 s and then continues at a constant speed of 26 m/s for a further 18 s. Calculate the total distance travelled.
520 m
Distance is the area under the speed-time graph: triangle area = ½ × 4 × 26 = 52 m, plus rectangle area = 18 × 26 = 468 m. Total distance = 52 + 468 = 520 m.
12. On a speed-time graph, a train accelerates uniformly from rest to 48 m/s in 11 s and then continues at a constant speed of 48 m/s for a further 5 s. Calculate the total distance travelled.
504 m
Distance is the area under the speed-time graph: triangle area = ½ × 11 × 48 = 264 m, plus rectangle area = 5 × 48 = 240 m. Total distance = 264 + 240 = 504 m.

12 questions · Seed 46 · 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 42 m/s in 10 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 = 10 s, t₂ = 13 s) · Distance = Area = ½vt₁ + vt₂
2. On a speed-time graph, a train accelerates uniformly from rest to 12 m/s in 2 s and then continues at a constant speed of 12 m/s for a further 19 s. Calculate the total distance travelled.
v_max = 12 m/s (t₁ = 2 s, t₂ = 19 s) · Distance = Area = ½vt₁ + vt₂
3. 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 15 s. Calculate the total distance travelled.
v_max = 46 m/s (t₁ = 9 s, t₂ = 15 s) · Distance = Area = ½vt₁ + vt₂
4. On a speed-time graph, a train accelerates uniformly from rest to 16 m/s in 4 s and then continues at a constant speed of 16 m/s for a further 13 s. Calculate the total distance travelled.
v_max = 16 m/s (t₁ = 4 s, t₂ = 13 s) · Distance = Area = ½vt₁ + vt₂
5. On a speed-time graph, a train accelerates uniformly from rest to 46 m/s in 5 s and then continues at a constant speed of 46 m/s for a further 4 s. Calculate the total distance travelled.
v_max = 46 m/s (t₁ = 5 s, t₂ = 4 s) · Distance = Area = ½vt₁ + vt₂
6. On a speed-time graph, a train accelerates uniformly from rest to 22 m/s in 10 s and then continues at a constant speed of 22 m/s for a further 10 s. Calculate the total distance travelled.
v_max = 22 m/s (t₁ = 10 s, t₂ = 10 s) · Distance = Area = ½vt₁ + vt₂
7. 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 12 s. Calculate the total distance travelled.
v_max = 22 m/s (t₁ = 3 s, t₂ = 12 s) · Distance = Area = ½vt₁ + vt₂
8. On a speed-time graph, a train accelerates uniformly from rest to 50 m/s in 3 s and then continues at a constant speed of 50 m/s for a further 20 s. Calculate the total distance travelled.
v_max = 50 m/s (t₁ = 3 s, t₂ = 20 s) · Distance = Area = ½vt₁ + vt₂
9. On a speed-time graph, a train accelerates uniformly from rest to 40 m/s in 6 s and then continues at a constant speed of 40 m/s for a further 13 s. Calculate the total distance travelled.
v_max = 40 m/s (t₁ = 6 s, t₂ = 13 s) · Distance = Area = ½vt₁ + vt₂
10. 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 16 s. Calculate the total distance travelled.
v_max = 12 m/s (t₁ = 4 s, t₂ = 16 s) · Distance = Area = ½vt₁ + vt₂
11. On a speed-time graph, a train accelerates uniformly from rest to 26 m/s in 4 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 = 4 s, t₂ = 18 s) · Distance = Area = ½vt₁ + vt₂
12. On a speed-time graph, a train accelerates uniformly from rest to 48 m/s in 11 s and then continues at a constant speed of 48 m/s for a further 5 s. Calculate the total distance travelled.
v_max = 48 m/s (t₁ = 11 s, t₂ = 5 s) · Distance = Area = ½vt₁ + vt₂

12 questions · Seed 46 · 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 42 m/s in 10 s and then continues at a constant speed of 42 m/s for a further 13 s. Calculate the total distance travelled.
756 m
Distance is the area under the speed-time graph: triangle area = ½ × 10 × 42 = 210 m, plus rectangle area = 13 × 42 = 546 m. Total distance = 210 + 546 = 756 m.
2. On a speed-time graph, a train accelerates uniformly from rest to 12 m/s in 2 s and then continues at a constant speed of 12 m/s for a further 19 s. Calculate the total distance travelled.
240 m
Distance is the area under the speed-time graph: triangle area = ½ × 2 × 12 = 12 m, plus rectangle area = 19 × 12 = 228 m. Total distance = 12 + 228 = 240 m.
3. 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 15 s. Calculate the total distance travelled.
897 m
Distance is the area under the speed-time graph: triangle area = ½ × 9 × 46 = 207 m, plus rectangle area = 15 × 46 = 690 m. Total distance = 207 + 690 = 897 m.
4. On a speed-time graph, a train accelerates uniformly from rest to 16 m/s in 4 s and then continues at a constant speed of 16 m/s for a further 13 s. Calculate the total distance travelled.
240 m
Distance is the area under the speed-time graph: triangle area = ½ × 4 × 16 = 32 m, plus rectangle area = 13 × 16 = 208 m. Total distance = 32 + 208 = 240 m.
5. On a speed-time graph, a train accelerates uniformly from rest to 46 m/s in 5 s and then continues at a constant speed of 46 m/s for a further 4 s. Calculate the total distance travelled.
299 m
Distance is the area under the speed-time graph: triangle area = ½ × 5 × 46 = 115 m, plus rectangle area = 4 × 46 = 184 m. Total distance = 115 + 184 = 299 m.
6. On a speed-time graph, a train accelerates uniformly from rest to 22 m/s in 10 s and then continues at a constant speed of 22 m/s for a further 10 s. Calculate the total distance travelled.
330 m
Distance is the area under the speed-time graph: triangle area = ½ × 10 × 22 = 110 m, plus rectangle area = 10 × 22 = 220 m. Total distance = 110 + 220 = 330 m.
7. 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 12 s. Calculate the total distance travelled.
297 m
Distance is the area under the speed-time graph: triangle area = ½ × 3 × 22 = 33 m, plus rectangle area = 12 × 22 = 264 m. Total distance = 33 + 264 = 297 m.
8. On a speed-time graph, a train accelerates uniformly from rest to 50 m/s in 3 s and then continues at a constant speed of 50 m/s for a further 20 s. Calculate the total distance travelled.
1075 m
Distance is the area under the speed-time graph: triangle area = ½ × 3 × 50 = 75 m, plus rectangle area = 20 × 50 = 1000 m. Total distance = 75 + 1000 = 1075 m.
9. On a speed-time graph, a train accelerates uniformly from rest to 40 m/s in 6 s and then continues at a constant speed of 40 m/s for a further 13 s. Calculate the total distance travelled.
640 m
Distance is the area under the speed-time graph: triangle area = ½ × 6 × 40 = 120 m, plus rectangle area = 13 × 40 = 520 m. Total distance = 120 + 520 = 640 m.
10. 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 16 s. Calculate the total distance travelled.
216 m
Distance is the area under the speed-time graph: triangle area = ½ × 4 × 12 = 24 m, plus rectangle area = 16 × 12 = 192 m. Total distance = 24 + 192 = 216 m.
11. On a speed-time graph, a train accelerates uniformly from rest to 26 m/s in 4 s and then continues at a constant speed of 26 m/s for a further 18 s. Calculate the total distance travelled.
520 m
Distance is the area under the speed-time graph: triangle area = ½ × 4 × 26 = 52 m, plus rectangle area = 18 × 26 = 468 m. Total distance = 52 + 468 = 520 m.
12. On a speed-time graph, a train accelerates uniformly from rest to 48 m/s in 11 s and then continues at a constant speed of 48 m/s for a further 5 s. Calculate the total distance travelled.
504 m
Distance is the area under the speed-time graph: triangle area = ½ × 11 × 48 = 264 m, plus rectangle area = 5 × 48 = 240 m. Total distance = 264 + 240 = 504 m.

12 questions · Seed 46 · Age guidance, not curriculum certification