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 48 m/s in 3 s and then continues at a constant speed of 48 m/s for a further 4 s. Calculate the total distance travelled.
v_max = 48 m/s (t₁ = 3 s, t₂ = 4 s) · Distance = Area = ½vt₁ + vt₂
2. On a speed-time graph, a train accelerates uniformly from rest to 34 m/s in 7 s and then continues at a constant speed of 34 m/s for a further 5 s. Calculate the total distance travelled.
v_max = 34 m/s (t₁ = 7 s, t₂ = 5 s) · Distance = Area = ½vt₁ + vt₂
3. On a speed-time graph, a train accelerates uniformly from rest to 22 m/s in 6 s and then continues at a constant speed of 22 m/s for a further 15 s. Calculate the total distance travelled.
v_max = 22 m/s (t₁ = 6 s, t₂ = 15 s) · Distance = Area = ½vt₁ + vt₂
4. On a speed-time graph, a train accelerates uniformly from rest to 48 m/s in 10 s and then continues at a constant speed of 48 m/s for a further 9 s. Calculate the total distance travelled.
v_max = 48 m/s (t₁ = 10 s, t₂ = 9 s) · Distance = Area = ½vt₁ + vt₂
5. On a speed-time graph, a train accelerates uniformly from rest to 24 m/s in 10 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 = 10 s, t₂ = 14 s) · Distance = Area = ½vt₁ + vt₂
6. On a speed-time graph, a train accelerates uniformly from rest to 12 m/s in 6 s and then continues at a constant speed of 12 m/s for a further 5 s. Calculate the total distance travelled.
v_max = 12 m/s (t₁ = 6 s, t₂ = 5 s) · Distance = Area = ½vt₁ + vt₂
7. On a speed-time graph, a train accelerates uniformly from rest to 16 m/s in 5 s and then continues at a constant speed of 16 m/s for a further 15 s. Calculate the total distance travelled.
v_max = 16 m/s (t₁ = 5 s, t₂ = 15 s) · Distance = Area = ½vt₁ + vt₂
8. On a speed-time graph, a train accelerates uniformly from rest to 28 m/s in 2 s and then continues at a constant speed of 28 m/s for a further 9 s. Calculate the total distance travelled.
v_max = 28 m/s (t₁ = 2 s, t₂ = 9 s) · Distance = Area = ½vt₁ + vt₂
9. 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 11 s. Calculate the total distance travelled.
v_max = 16 m/s (t₁ = 2 s, t₂ = 11 s) · Distance = Area = ½vt₁ + vt₂
10. 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 16 s. Calculate the total distance travelled.
v_max = 30 m/s (t₁ = 9 s, t₂ = 16 s) · Distance = Area = ½vt₁ + vt₂
11. 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 13 s. Calculate the total distance travelled.
v_max = 30 m/s (t₁ = 5 s, t₂ = 13 s) · Distance = Area = ½vt₁ + vt₂
12. On a speed-time graph, a train accelerates uniformly from rest to 36 m/s in 10 s and then continues at a constant speed of 36 m/s for a further 6 s. Calculate the total distance travelled.
v_max = 36 m/s (t₁ = 10 s, t₂ = 6 s) · Distance = Area = ½vt₁ + vt₂

12 questions · Seed 104740 · 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 48 m/s in 3 s and then continues at a constant speed of 48 m/s for a further 4 s. Calculate the total distance travelled.
264 m
Distance is the area under the speed-time graph: triangle area = ½ × 3 × 48 = 72 m, plus rectangle area = 4 × 48 = 192 m. Total distance = 72 + 192 = 264 m.
2. On a speed-time graph, a train accelerates uniformly from rest to 34 m/s in 7 s and then continues at a constant speed of 34 m/s for a further 5 s. Calculate the total distance travelled.
289 m
Distance is the area under the speed-time graph: triangle area = ½ × 7 × 34 = 119 m, plus rectangle area = 5 × 34 = 170 m. Total distance = 119 + 170 = 289 m.
3. On a speed-time graph, a train accelerates uniformly from rest to 22 m/s in 6 s and then continues at a constant speed of 22 m/s for a further 15 s. Calculate the total distance travelled.
396 m
Distance is the area under the speed-time graph: triangle area = ½ × 6 × 22 = 66 m, plus rectangle area = 15 × 22 = 330 m. Total distance = 66 + 330 = 396 m.
4. On a speed-time graph, a train accelerates uniformly from rest to 48 m/s in 10 s and then continues at a constant speed of 48 m/s for a further 9 s. Calculate the total distance travelled.
672 m
Distance is the area under the speed-time graph: triangle area = ½ × 10 × 48 = 240 m, plus rectangle area = 9 × 48 = 432 m. Total distance = 240 + 432 = 672 m.
5. On a speed-time graph, a train accelerates uniformly from rest to 24 m/s in 10 s and then continues at a constant speed of 24 m/s for a further 14 s. Calculate the total distance travelled.
456 m
Distance is the area under the speed-time graph: triangle area = ½ × 10 × 24 = 120 m, plus rectangle area = 14 × 24 = 336 m. Total distance = 120 + 336 = 456 m.
6. On a speed-time graph, a train accelerates uniformly from rest to 12 m/s in 6 s and then continues at a constant speed of 12 m/s for a further 5 s. Calculate the total distance travelled.
96 m
Distance is the area under the speed-time graph: triangle area = ½ × 6 × 12 = 36 m, plus rectangle area = 5 × 12 = 60 m. Total distance = 36 + 60 = 96 m.
7. On a speed-time graph, a train accelerates uniformly from rest to 16 m/s in 5 s and then continues at a constant speed of 16 m/s for a further 15 s. Calculate the total distance travelled.
280 m
Distance is the area under the speed-time graph: triangle area = ½ × 5 × 16 = 40 m, plus rectangle area = 15 × 16 = 240 m. Total distance = 40 + 240 = 280 m.
8. On a speed-time graph, a train accelerates uniformly from rest to 28 m/s in 2 s and then continues at a constant speed of 28 m/s for a further 9 s. Calculate the total distance travelled.
280 m
Distance is the area under the speed-time graph: triangle area = ½ × 2 × 28 = 28 m, plus rectangle area = 9 × 28 = 252 m. Total distance = 28 + 252 = 280 m.
9. 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 11 s. Calculate the total distance travelled.
192 m
Distance is the area under the speed-time graph: triangle area = ½ × 2 × 16 = 16 m, plus rectangle area = 11 × 16 = 176 m. Total distance = 16 + 176 = 192 m.
10. 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 16 s. Calculate the total distance travelled.
615 m
Distance is the area under the speed-time graph: triangle area = ½ × 9 × 30 = 135 m, plus rectangle area = 16 × 30 = 480 m. Total distance = 135 + 480 = 615 m.
11. 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 13 s. Calculate the total distance travelled.
465 m
Distance is the area under the speed-time graph: triangle area = ½ × 5 × 30 = 75 m, plus rectangle area = 13 × 30 = 390 m. Total distance = 75 + 390 = 465 m.
12. On a speed-time graph, a train accelerates uniformly from rest to 36 m/s in 10 s and then continues at a constant speed of 36 m/s for a further 6 s. Calculate the total distance travelled.
396 m
Distance is the area under the speed-time graph: triangle area = ½ × 10 × 36 = 180 m, plus rectangle area = 6 × 36 = 216 m. Total distance = 180 + 216 = 396 m.

12 questions · Seed 104740 · 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 48 m/s in 3 s and then continues at a constant speed of 48 m/s for a further 4 s. Calculate the total distance travelled.
v_max = 48 m/s (t₁ = 3 s, t₂ = 4 s) · Distance = Area = ½vt₁ + vt₂
2. On a speed-time graph, a train accelerates uniformly from rest to 34 m/s in 7 s and then continues at a constant speed of 34 m/s for a further 5 s. Calculate the total distance travelled.
v_max = 34 m/s (t₁ = 7 s, t₂ = 5 s) · Distance = Area = ½vt₁ + vt₂
3. On a speed-time graph, a train accelerates uniformly from rest to 22 m/s in 6 s and then continues at a constant speed of 22 m/s for a further 15 s. Calculate the total distance travelled.
v_max = 22 m/s (t₁ = 6 s, t₂ = 15 s) · Distance = Area = ½vt₁ + vt₂
4. On a speed-time graph, a train accelerates uniformly from rest to 48 m/s in 10 s and then continues at a constant speed of 48 m/s for a further 9 s. Calculate the total distance travelled.
v_max = 48 m/s (t₁ = 10 s, t₂ = 9 s) · Distance = Area = ½vt₁ + vt₂
5. On a speed-time graph, a train accelerates uniformly from rest to 24 m/s in 10 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 = 10 s, t₂ = 14 s) · Distance = Area = ½vt₁ + vt₂
6. On a speed-time graph, a train accelerates uniformly from rest to 12 m/s in 6 s and then continues at a constant speed of 12 m/s for a further 5 s. Calculate the total distance travelled.
v_max = 12 m/s (t₁ = 6 s, t₂ = 5 s) · Distance = Area = ½vt₁ + vt₂
7. On a speed-time graph, a train accelerates uniformly from rest to 16 m/s in 5 s and then continues at a constant speed of 16 m/s for a further 15 s. Calculate the total distance travelled.
v_max = 16 m/s (t₁ = 5 s, t₂ = 15 s) · Distance = Area = ½vt₁ + vt₂
8. On a speed-time graph, a train accelerates uniformly from rest to 28 m/s in 2 s and then continues at a constant speed of 28 m/s for a further 9 s. Calculate the total distance travelled.
v_max = 28 m/s (t₁ = 2 s, t₂ = 9 s) · Distance = Area = ½vt₁ + vt₂
9. 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 11 s. Calculate the total distance travelled.
v_max = 16 m/s (t₁ = 2 s, t₂ = 11 s) · Distance = Area = ½vt₁ + vt₂
10. 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 16 s. Calculate the total distance travelled.
v_max = 30 m/s (t₁ = 9 s, t₂ = 16 s) · Distance = Area = ½vt₁ + vt₂
11. 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 13 s. Calculate the total distance travelled.
v_max = 30 m/s (t₁ = 5 s, t₂ = 13 s) · Distance = Area = ½vt₁ + vt₂
12. On a speed-time graph, a train accelerates uniformly from rest to 36 m/s in 10 s and then continues at a constant speed of 36 m/s for a further 6 s. Calculate the total distance travelled.
v_max = 36 m/s (t₁ = 10 s, t₂ = 6 s) · Distance = Area = ½vt₁ + vt₂

12 questions · Seed 104740 · 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 48 m/s in 3 s and then continues at a constant speed of 48 m/s for a further 4 s. Calculate the total distance travelled.
264 m
Distance is the area under the speed-time graph: triangle area = ½ × 3 × 48 = 72 m, plus rectangle area = 4 × 48 = 192 m. Total distance = 72 + 192 = 264 m.
2. On a speed-time graph, a train accelerates uniformly from rest to 34 m/s in 7 s and then continues at a constant speed of 34 m/s for a further 5 s. Calculate the total distance travelled.
289 m
Distance is the area under the speed-time graph: triangle area = ½ × 7 × 34 = 119 m, plus rectangle area = 5 × 34 = 170 m. Total distance = 119 + 170 = 289 m.
3. On a speed-time graph, a train accelerates uniformly from rest to 22 m/s in 6 s and then continues at a constant speed of 22 m/s for a further 15 s. Calculate the total distance travelled.
396 m
Distance is the area under the speed-time graph: triangle area = ½ × 6 × 22 = 66 m, plus rectangle area = 15 × 22 = 330 m. Total distance = 66 + 330 = 396 m.
4. On a speed-time graph, a train accelerates uniformly from rest to 48 m/s in 10 s and then continues at a constant speed of 48 m/s for a further 9 s. Calculate the total distance travelled.
672 m
Distance is the area under the speed-time graph: triangle area = ½ × 10 × 48 = 240 m, plus rectangle area = 9 × 48 = 432 m. Total distance = 240 + 432 = 672 m.
5. On a speed-time graph, a train accelerates uniformly from rest to 24 m/s in 10 s and then continues at a constant speed of 24 m/s for a further 14 s. Calculate the total distance travelled.
456 m
Distance is the area under the speed-time graph: triangle area = ½ × 10 × 24 = 120 m, plus rectangle area = 14 × 24 = 336 m. Total distance = 120 + 336 = 456 m.
6. On a speed-time graph, a train accelerates uniformly from rest to 12 m/s in 6 s and then continues at a constant speed of 12 m/s for a further 5 s. Calculate the total distance travelled.
96 m
Distance is the area under the speed-time graph: triangle area = ½ × 6 × 12 = 36 m, plus rectangle area = 5 × 12 = 60 m. Total distance = 36 + 60 = 96 m.
7. On a speed-time graph, a train accelerates uniformly from rest to 16 m/s in 5 s and then continues at a constant speed of 16 m/s for a further 15 s. Calculate the total distance travelled.
280 m
Distance is the area under the speed-time graph: triangle area = ½ × 5 × 16 = 40 m, plus rectangle area = 15 × 16 = 240 m. Total distance = 40 + 240 = 280 m.
8. On a speed-time graph, a train accelerates uniformly from rest to 28 m/s in 2 s and then continues at a constant speed of 28 m/s for a further 9 s. Calculate the total distance travelled.
280 m
Distance is the area under the speed-time graph: triangle area = ½ × 2 × 28 = 28 m, plus rectangle area = 9 × 28 = 252 m. Total distance = 28 + 252 = 280 m.
9. 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 11 s. Calculate the total distance travelled.
192 m
Distance is the area under the speed-time graph: triangle area = ½ × 2 × 16 = 16 m, plus rectangle area = 11 × 16 = 176 m. Total distance = 16 + 176 = 192 m.
10. 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 16 s. Calculate the total distance travelled.
615 m
Distance is the area under the speed-time graph: triangle area = ½ × 9 × 30 = 135 m, plus rectangle area = 16 × 30 = 480 m. Total distance = 135 + 480 = 615 m.
11. 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 13 s. Calculate the total distance travelled.
465 m
Distance is the area under the speed-time graph: triangle area = ½ × 5 × 30 = 75 m, plus rectangle area = 13 × 30 = 390 m. Total distance = 75 + 390 = 465 m.
12. On a speed-time graph, a train accelerates uniformly from rest to 36 m/s in 10 s and then continues at a constant speed of 36 m/s for a further 6 s. Calculate the total distance travelled.
396 m
Distance is the area under the speed-time graph: triangle area = ½ × 10 × 36 = 180 m, plus rectangle area = 6 × 36 = 216 m. Total distance = 180 + 216 = 396 m.

12 questions · Seed 104740 · Age guidance, not curriculum certification