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 9 s. Calculate the total distance travelled.
v_max = 36 m/s (t₁ = 8 s, t₂ = 9 s) · Distance = Area = ½vt₁ + vt₂
2. On a speed-time graph, a train accelerates uniformly from rest to 30 m/s in 5 s and then continues at a constant speed of 30 m/s for a further 15 s. Calculate the total distance travelled.
v_max = 30 m/s (t₁ = 5 s, t₂ = 15 s) · Distance = Area = ½vt₁ + vt₂
3. On a speed-time graph, a train accelerates uniformly from rest to 18 m/s in 10 s and then continues at a constant speed of 18 m/s for a further 19 s. Calculate the total distance travelled.
v_max = 18 m/s (t₁ = 10 s, t₂ = 19 s) · Distance = Area = ½vt₁ + vt₂
4. On a speed-time graph, a train accelerates uniformly from rest to 34 m/s in 10 s and then continues at a constant speed of 34 m/s for a further 16 s. Calculate the total distance travelled.
v_max = 34 m/s (t₁ = 10 s, t₂ = 16 s) · Distance = Area = ½vt₁ + vt₂
5. On a speed-time graph, a train accelerates uniformly from rest to 18 m/s in 4 s and then continues at a constant speed of 18 m/s for a further 12 s. Calculate the total distance travelled.
v_max = 18 m/s (t₁ = 4 s, t₂ = 12 s) · Distance = Area = ½vt₁ + vt₂
6. 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 6 s. Calculate the total distance travelled.
v_max = 14 m/s (t₁ = 6 s, t₂ = 6 s) · Distance = Area = ½vt₁ + vt₂
7. 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 6 s. Calculate the total distance travelled.
v_max = 28 m/s (t₁ = 8 s, t₂ = 6 s) · Distance = Area = ½vt₁ + vt₂
8. 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 18 s. Calculate the total distance travelled.
v_max = 26 m/s (t₁ = 9 s, t₂ = 18 s) · Distance = Area = ½vt₁ + vt₂
9. 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 9 s. Calculate the total distance travelled.
v_max = 8 m/s (t₁ = 6 s, t₂ = 9 s) · Distance = Area = ½vt₁ + vt₂
10. On a speed-time graph, a train accelerates uniformly from rest to 14 m/s in 4 s and then continues at a constant speed of 14 m/s for a further 20 s. Calculate the total distance travelled.
v_max = 14 m/s (t₁ = 4 s, t₂ = 20 s) · Distance = Area = ½vt₁ + vt₂
11. On a speed-time graph, a train accelerates uniformly from rest to 18 m/s in 11 s and then continues at a constant speed of 18 m/s for a further 12 s. Calculate the total distance travelled.
v_max = 18 m/s (t₁ = 11 s, t₂ = 12 s) · Distance = Area = ½vt₁ + vt₂
12. On a speed-time graph, a train accelerates uniformly from rest to 24 m/s in 12 s and then continues at a constant speed of 24 m/s for a further 14 s. Calculate the total distance travelled.
v_max = 24 m/s (t₁ = 12 s, t₂ = 14 s) · Distance = Area = ½vt₁ + vt₂

12 questions · Seed 104730 · 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 9 s. Calculate the total distance travelled.
468 m
Distance is the area under the speed-time graph: triangle area = ½ × 8 × 36 = 144 m, plus rectangle area = 9 × 36 = 324 m. Total distance = 144 + 324 = 468 m.
2. On a speed-time graph, a train accelerates uniformly from rest to 30 m/s in 5 s and then continues at a constant speed of 30 m/s for a further 15 s. Calculate the total distance travelled.
525 m
Distance is the area under the speed-time graph: triangle area = ½ × 5 × 30 = 75 m, plus rectangle area = 15 × 30 = 450 m. Total distance = 75 + 450 = 525 m.
3. On a speed-time graph, a train accelerates uniformly from rest to 18 m/s in 10 s and then continues at a constant speed of 18 m/s for a further 19 s. Calculate the total distance travelled.
432 m
Distance is the area under the speed-time graph: triangle area = ½ × 10 × 18 = 90 m, plus rectangle area = 19 × 18 = 342 m. Total distance = 90 + 342 = 432 m.
4. On a speed-time graph, a train accelerates uniformly from rest to 34 m/s in 10 s and then continues at a constant speed of 34 m/s for a further 16 s. Calculate the total distance travelled.
714 m
Distance is the area under the speed-time graph: triangle area = ½ × 10 × 34 = 170 m, plus rectangle area = 16 × 34 = 544 m. Total distance = 170 + 544 = 714 m.
5. On a speed-time graph, a train accelerates uniformly from rest to 18 m/s in 4 s and then continues at a constant speed of 18 m/s for a further 12 s. Calculate the total distance travelled.
252 m
Distance is the area under the speed-time graph: triangle area = ½ × 4 × 18 = 36 m, plus rectangle area = 12 × 18 = 216 m. Total distance = 36 + 216 = 252 m.
6. 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 6 s. Calculate the total distance travelled.
126 m
Distance is the area under the speed-time graph: triangle area = ½ × 6 × 14 = 42 m, plus rectangle area = 6 × 14 = 84 m. Total distance = 42 + 84 = 126 m.
7. 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 6 s. Calculate the total distance travelled.
280 m
Distance is the area under the speed-time graph: triangle area = ½ × 8 × 28 = 112 m, plus rectangle area = 6 × 28 = 168 m. Total distance = 112 + 168 = 280 m.
8. 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 18 s. Calculate the total distance travelled.
585 m
Distance is the area under the speed-time graph: triangle area = ½ × 9 × 26 = 117 m, plus rectangle area = 18 × 26 = 468 m. Total distance = 117 + 468 = 585 m.
9. 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 9 s. Calculate the total distance travelled.
96 m
Distance is the area under the speed-time graph: triangle area = ½ × 6 × 8 = 24 m, plus rectangle area = 9 × 8 = 72 m. Total distance = 24 + 72 = 96 m.
10. On a speed-time graph, a train accelerates uniformly from rest to 14 m/s in 4 s and then continues at a constant speed of 14 m/s for a further 20 s. Calculate the total distance travelled.
308 m
Distance is the area under the speed-time graph: triangle area = ½ × 4 × 14 = 28 m, plus rectangle area = 20 × 14 = 280 m. Total distance = 28 + 280 = 308 m.
11. On a speed-time graph, a train accelerates uniformly from rest to 18 m/s in 11 s and then continues at a constant speed of 18 m/s for a further 12 s. Calculate the total distance travelled.
315 m
Distance is the area under the speed-time graph: triangle area = ½ × 11 × 18 = 99 m, plus rectangle area = 12 × 18 = 216 m. Total distance = 99 + 216 = 315 m.
12. On a speed-time graph, a train accelerates uniformly from rest to 24 m/s in 12 s and then continues at a constant speed of 24 m/s for a further 14 s. Calculate the total distance travelled.
480 m
Distance is the area under the speed-time graph: triangle area = ½ × 12 × 24 = 144 m, plus rectangle area = 14 × 24 = 336 m. Total distance = 144 + 336 = 480 m.

12 questions · Seed 104730 · 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 9 s. Calculate the total distance travelled.
v_max = 36 m/s (t₁ = 8 s, t₂ = 9 s) · Distance = Area = ½vt₁ + vt₂
2. On a speed-time graph, a train accelerates uniformly from rest to 30 m/s in 5 s and then continues at a constant speed of 30 m/s for a further 15 s. Calculate the total distance travelled.
v_max = 30 m/s (t₁ = 5 s, t₂ = 15 s) · Distance = Area = ½vt₁ + vt₂
3. On a speed-time graph, a train accelerates uniformly from rest to 18 m/s in 10 s and then continues at a constant speed of 18 m/s for a further 19 s. Calculate the total distance travelled.
v_max = 18 m/s (t₁ = 10 s, t₂ = 19 s) · Distance = Area = ½vt₁ + vt₂
4. On a speed-time graph, a train accelerates uniformly from rest to 34 m/s in 10 s and then continues at a constant speed of 34 m/s for a further 16 s. Calculate the total distance travelled.
v_max = 34 m/s (t₁ = 10 s, t₂ = 16 s) · Distance = Area = ½vt₁ + vt₂
5. On a speed-time graph, a train accelerates uniformly from rest to 18 m/s in 4 s and then continues at a constant speed of 18 m/s for a further 12 s. Calculate the total distance travelled.
v_max = 18 m/s (t₁ = 4 s, t₂ = 12 s) · Distance = Area = ½vt₁ + vt₂
6. 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 6 s. Calculate the total distance travelled.
v_max = 14 m/s (t₁ = 6 s, t₂ = 6 s) · Distance = Area = ½vt₁ + vt₂
7. 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 6 s. Calculate the total distance travelled.
v_max = 28 m/s (t₁ = 8 s, t₂ = 6 s) · Distance = Area = ½vt₁ + vt₂
8. 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 18 s. Calculate the total distance travelled.
v_max = 26 m/s (t₁ = 9 s, t₂ = 18 s) · Distance = Area = ½vt₁ + vt₂
9. 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 9 s. Calculate the total distance travelled.
v_max = 8 m/s (t₁ = 6 s, t₂ = 9 s) · Distance = Area = ½vt₁ + vt₂
10. On a speed-time graph, a train accelerates uniformly from rest to 14 m/s in 4 s and then continues at a constant speed of 14 m/s for a further 20 s. Calculate the total distance travelled.
v_max = 14 m/s (t₁ = 4 s, t₂ = 20 s) · Distance = Area = ½vt₁ + vt₂
11. On a speed-time graph, a train accelerates uniformly from rest to 18 m/s in 11 s and then continues at a constant speed of 18 m/s for a further 12 s. Calculate the total distance travelled.
v_max = 18 m/s (t₁ = 11 s, t₂ = 12 s) · Distance = Area = ½vt₁ + vt₂
12. On a speed-time graph, a train accelerates uniformly from rest to 24 m/s in 12 s and then continues at a constant speed of 24 m/s for a further 14 s. Calculate the total distance travelled.
v_max = 24 m/s (t₁ = 12 s, t₂ = 14 s) · Distance = Area = ½vt₁ + vt₂

12 questions · Seed 104730 · 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 9 s. Calculate the total distance travelled.
468 m
Distance is the area under the speed-time graph: triangle area = ½ × 8 × 36 = 144 m, plus rectangle area = 9 × 36 = 324 m. Total distance = 144 + 324 = 468 m.
2. On a speed-time graph, a train accelerates uniformly from rest to 30 m/s in 5 s and then continues at a constant speed of 30 m/s for a further 15 s. Calculate the total distance travelled.
525 m
Distance is the area under the speed-time graph: triangle area = ½ × 5 × 30 = 75 m, plus rectangle area = 15 × 30 = 450 m. Total distance = 75 + 450 = 525 m.
3. On a speed-time graph, a train accelerates uniformly from rest to 18 m/s in 10 s and then continues at a constant speed of 18 m/s for a further 19 s. Calculate the total distance travelled.
432 m
Distance is the area under the speed-time graph: triangle area = ½ × 10 × 18 = 90 m, plus rectangle area = 19 × 18 = 342 m. Total distance = 90 + 342 = 432 m.
4. On a speed-time graph, a train accelerates uniformly from rest to 34 m/s in 10 s and then continues at a constant speed of 34 m/s for a further 16 s. Calculate the total distance travelled.
714 m
Distance is the area under the speed-time graph: triangle area = ½ × 10 × 34 = 170 m, plus rectangle area = 16 × 34 = 544 m. Total distance = 170 + 544 = 714 m.
5. On a speed-time graph, a train accelerates uniformly from rest to 18 m/s in 4 s and then continues at a constant speed of 18 m/s for a further 12 s. Calculate the total distance travelled.
252 m
Distance is the area under the speed-time graph: triangle area = ½ × 4 × 18 = 36 m, plus rectangle area = 12 × 18 = 216 m. Total distance = 36 + 216 = 252 m.
6. 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 6 s. Calculate the total distance travelled.
126 m
Distance is the area under the speed-time graph: triangle area = ½ × 6 × 14 = 42 m, plus rectangle area = 6 × 14 = 84 m. Total distance = 42 + 84 = 126 m.
7. 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 6 s. Calculate the total distance travelled.
280 m
Distance is the area under the speed-time graph: triangle area = ½ × 8 × 28 = 112 m, plus rectangle area = 6 × 28 = 168 m. Total distance = 112 + 168 = 280 m.
8. 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 18 s. Calculate the total distance travelled.
585 m
Distance is the area under the speed-time graph: triangle area = ½ × 9 × 26 = 117 m, plus rectangle area = 18 × 26 = 468 m. Total distance = 117 + 468 = 585 m.
9. 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 9 s. Calculate the total distance travelled.
96 m
Distance is the area under the speed-time graph: triangle area = ½ × 6 × 8 = 24 m, plus rectangle area = 9 × 8 = 72 m. Total distance = 24 + 72 = 96 m.
10. On a speed-time graph, a train accelerates uniformly from rest to 14 m/s in 4 s and then continues at a constant speed of 14 m/s for a further 20 s. Calculate the total distance travelled.
308 m
Distance is the area under the speed-time graph: triangle area = ½ × 4 × 14 = 28 m, plus rectangle area = 20 × 14 = 280 m. Total distance = 28 + 280 = 308 m.
11. On a speed-time graph, a train accelerates uniformly from rest to 18 m/s in 11 s and then continues at a constant speed of 18 m/s for a further 12 s. Calculate the total distance travelled.
315 m
Distance is the area under the speed-time graph: triangle area = ½ × 11 × 18 = 99 m, plus rectangle area = 12 × 18 = 216 m. Total distance = 99 + 216 = 315 m.
12. On a speed-time graph, a train accelerates uniformly from rest to 24 m/s in 12 s and then continues at a constant speed of 24 m/s for a further 14 s. Calculate the total distance travelled.
480 m
Distance is the area under the speed-time graph: triangle area = ½ × 12 × 24 = 144 m, plus rectangle area = 14 × 24 = 336 m. Total distance = 144 + 336 = 480 m.

12 questions · Seed 104730 · Age guidance, not curriculum certification