ScienceAges 13-15

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 13-15

Speed-time graphs: area & distance

Take your time. Show your thinking.

1. On a speed-time graph, a train accelerates uniformly from rest to 12 m/s in 11 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 = 11 s, t₂ = 11 s) · Distance = Area = ½vt₁ + vt₂
2. 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 14 s. Calculate the total distance travelled.
v_max = 12 m/s (t₁ = 6 s, t₂ = 14 s) · Distance = Area = ½vt₁ + vt₂
3. On a speed-time graph, a train accelerates uniformly from rest to 48 m/s in 6 s and then continues at a constant speed of 48 m/s for a further 13 s. Calculate the total distance travelled.
v_max = 48 m/s (t₁ = 6 s, t₂ = 13 s) · Distance = Area = ½vt₁ + vt₂
4. On a speed-time graph, a train accelerates uniformly from rest to 34 m/s in 3 s and then continues at a constant speed of 34 m/s for a further 8 s. Calculate the total distance travelled.
v_max = 34 m/s (t₁ = 3 s, t₂ = 8 s) · Distance = Area = ½vt₁ + vt₂
5. On a speed-time graph, a train accelerates uniformly from rest to 40 m/s in 7 s and then continues at a constant speed of 40 m/s for a further 9 s. Calculate the total distance travelled.
v_max = 40 m/s (t₁ = 7 s, t₂ = 9 s) · Distance = Area = ½vt₁ + vt₂
6. On a speed-time graph, a train accelerates uniformly from rest to 20 m/s in 9 s and then continues at a constant speed of 20 m/s for a further 14 s. Calculate the total distance travelled.
v_max = 20 m/s (t₁ = 9 s, t₂ = 14 s) · Distance = Area = ½vt₁ + vt₂
7. On a speed-time graph, a train accelerates uniformly from rest to 34 m/s in 4 s and then continues at a constant speed of 34 m/s for a further 20 s. Calculate the total distance travelled.
v_max = 34 m/s (t₁ = 4 s, t₂ = 20 s) · Distance = Area = ½vt₁ + vt₂
8. On a speed-time graph, a train accelerates uniformly from rest to 34 m/s in 2 s and then continues at a constant speed of 34 m/s for a further 6 s. Calculate the total distance travelled.
v_max = 34 m/s (t₁ = 2 s, t₂ = 6 s) · Distance = Area = ½vt₁ + vt₂
9. On a speed-time graph, a train accelerates uniformly from rest to 48 m/s in 12 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 = 12 s, t₂ = 4 s) · Distance = Area = ½vt₁ + vt₂
10. On a speed-time graph, a train accelerates uniformly from rest to 14 m/s in 9 s and then continues at a constant speed of 14 m/s for a further 16 s. Calculate the total distance travelled.
v_max = 14 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 12 m/s in 6 s and then continues at a constant speed of 12 m/s for a further 12 s. Calculate the total distance travelled.
v_max = 12 m/s (t₁ = 6 s, t₂ = 12 s) · Distance = Area = ½vt₁ + vt₂
12. 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 20 s. Calculate the total distance travelled.
v_max = 48 m/s (t₁ = 5 s, t₂ = 20 s) · Distance = Area = ½vt₁ + vt₂

12 questions · Seed 50 · Age guidance, not curriculum certification

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Worksheet StudioAnswer key · Ages 13-15

Speed-time graphs: area & distance

Answers and reasoning. Review before teaching.

1. On a speed-time graph, a train accelerates uniformly from rest to 12 m/s in 11 s and then continues at a constant speed of 12 m/s for a further 11 s. Calculate the total distance travelled.
198 m
Distance is the area under the speed-time graph: triangle area = ½ × 11 × 12 = 66 m, plus rectangle area = 11 × 12 = 132 m. Total distance = 66 + 132 = 198 m.
2. 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 14 s. Calculate the total distance travelled.
204 m
Distance is the area under the speed-time graph: triangle area = ½ × 6 × 12 = 36 m, plus rectangle area = 14 × 12 = 168 m. Total distance = 36 + 168 = 204 m.
3. On a speed-time graph, a train accelerates uniformly from rest to 48 m/s in 6 s and then continues at a constant speed of 48 m/s for a further 13 s. Calculate the total distance travelled.
768 m
Distance is the area under the speed-time graph: triangle area = ½ × 6 × 48 = 144 m, plus rectangle area = 13 × 48 = 624 m. Total distance = 144 + 624 = 768 m.
4. On a speed-time graph, a train accelerates uniformly from rest to 34 m/s in 3 s and then continues at a constant speed of 34 m/s for a further 8 s. Calculate the total distance travelled.
323 m
Distance is the area under the speed-time graph: triangle area = ½ × 3 × 34 = 51 m, plus rectangle area = 8 × 34 = 272 m. Total distance = 51 + 272 = 323 m.
5. On a speed-time graph, a train accelerates uniformly from rest to 40 m/s in 7 s and then continues at a constant speed of 40 m/s for a further 9 s. Calculate the total distance travelled.
500 m
Distance is the area under the speed-time graph: triangle area = ½ × 7 × 40 = 140 m, plus rectangle area = 9 × 40 = 360 m. Total distance = 140 + 360 = 500 m.
6. On a speed-time graph, a train accelerates uniformly from rest to 20 m/s in 9 s and then continues at a constant speed of 20 m/s for a further 14 s. Calculate the total distance travelled.
370 m
Distance is the area under the speed-time graph: triangle area = ½ × 9 × 20 = 90 m, plus rectangle area = 14 × 20 = 280 m. Total distance = 90 + 280 = 370 m.
7. On a speed-time graph, a train accelerates uniformly from rest to 34 m/s in 4 s and then continues at a constant speed of 34 m/s for a further 20 s. Calculate the total distance travelled.
748 m
Distance is the area under the speed-time graph: triangle area = ½ × 4 × 34 = 68 m, plus rectangle area = 20 × 34 = 680 m. Total distance = 68 + 680 = 748 m.
8. On a speed-time graph, a train accelerates uniformly from rest to 34 m/s in 2 s and then continues at a constant speed of 34 m/s for a further 6 s. Calculate the total distance travelled.
238 m
Distance is the area under the speed-time graph: triangle area = ½ × 2 × 34 = 34 m, plus rectangle area = 6 × 34 = 204 m. Total distance = 34 + 204 = 238 m.
9. On a speed-time graph, a train accelerates uniformly from rest to 48 m/s in 12 s and then continues at a constant speed of 48 m/s for a further 4 s. Calculate the total distance travelled.
480 m
Distance is the area under the speed-time graph: triangle area = ½ × 12 × 48 = 288 m, plus rectangle area = 4 × 48 = 192 m. Total distance = 288 + 192 = 480 m.
10. On a speed-time graph, a train accelerates uniformly from rest to 14 m/s in 9 s and then continues at a constant speed of 14 m/s for a further 16 s. Calculate the total distance travelled.
287 m
Distance is the area under the speed-time graph: triangle area = ½ × 9 × 14 = 63 m, plus rectangle area = 16 × 14 = 224 m. Total distance = 63 + 224 = 287 m.
11. 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 12 s. Calculate the total distance travelled.
180 m
Distance is the area under the speed-time graph: triangle area = ½ × 6 × 12 = 36 m, plus rectangle area = 12 × 12 = 144 m. Total distance = 36 + 144 = 180 m.
12. 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 20 s. Calculate the total distance travelled.
1080 m
Distance is the area under the speed-time graph: triangle area = ½ × 5 × 48 = 120 m, plus rectangle area = 20 × 48 = 960 m. Total distance = 120 + 960 = 1080 m.

12 questions · Seed 50 · Age guidance, not curriculum certification

Worksheet StudioPractice pack · Ages 13-15

Speed-time graphs: area & distance

Take your time. Show your thinking.

1. On a speed-time graph, a train accelerates uniformly from rest to 12 m/s in 11 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 = 11 s, t₂ = 11 s) · Distance = Area = ½vt₁ + vt₂
2. 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 14 s. Calculate the total distance travelled.
v_max = 12 m/s (t₁ = 6 s, t₂ = 14 s) · Distance = Area = ½vt₁ + vt₂
3. On a speed-time graph, a train accelerates uniformly from rest to 48 m/s in 6 s and then continues at a constant speed of 48 m/s for a further 13 s. Calculate the total distance travelled.
v_max = 48 m/s (t₁ = 6 s, t₂ = 13 s) · Distance = Area = ½vt₁ + vt₂
4. On a speed-time graph, a train accelerates uniformly from rest to 34 m/s in 3 s and then continues at a constant speed of 34 m/s for a further 8 s. Calculate the total distance travelled.
v_max = 34 m/s (t₁ = 3 s, t₂ = 8 s) · Distance = Area = ½vt₁ + vt₂
5. On a speed-time graph, a train accelerates uniformly from rest to 40 m/s in 7 s and then continues at a constant speed of 40 m/s for a further 9 s. Calculate the total distance travelled.
v_max = 40 m/s (t₁ = 7 s, t₂ = 9 s) · Distance = Area = ½vt₁ + vt₂
6. On a speed-time graph, a train accelerates uniformly from rest to 20 m/s in 9 s and then continues at a constant speed of 20 m/s for a further 14 s. Calculate the total distance travelled.
v_max = 20 m/s (t₁ = 9 s, t₂ = 14 s) · Distance = Area = ½vt₁ + vt₂
7. On a speed-time graph, a train accelerates uniformly from rest to 34 m/s in 4 s and then continues at a constant speed of 34 m/s for a further 20 s. Calculate the total distance travelled.
v_max = 34 m/s (t₁ = 4 s, t₂ = 20 s) · Distance = Area = ½vt₁ + vt₂
8. On a speed-time graph, a train accelerates uniformly from rest to 34 m/s in 2 s and then continues at a constant speed of 34 m/s for a further 6 s. Calculate the total distance travelled.
v_max = 34 m/s (t₁ = 2 s, t₂ = 6 s) · Distance = Area = ½vt₁ + vt₂
9. On a speed-time graph, a train accelerates uniformly from rest to 48 m/s in 12 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 = 12 s, t₂ = 4 s) · Distance = Area = ½vt₁ + vt₂
10. On a speed-time graph, a train accelerates uniformly from rest to 14 m/s in 9 s and then continues at a constant speed of 14 m/s for a further 16 s. Calculate the total distance travelled.
v_max = 14 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 12 m/s in 6 s and then continues at a constant speed of 12 m/s for a further 12 s. Calculate the total distance travelled.
v_max = 12 m/s (t₁ = 6 s, t₂ = 12 s) · Distance = Area = ½vt₁ + vt₂
12. 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 20 s. Calculate the total distance travelled.
v_max = 48 m/s (t₁ = 5 s, t₂ = 20 s) · Distance = Area = ½vt₁ + vt₂

12 questions · Seed 50 · Age guidance, not curriculum certification

Worksheet StudioAnswer key · Ages 13-15

Speed-time graphs: area & distance

Answers and reasoning. Review before teaching.

1. On a speed-time graph, a train accelerates uniformly from rest to 12 m/s in 11 s and then continues at a constant speed of 12 m/s for a further 11 s. Calculate the total distance travelled.
198 m
Distance is the area under the speed-time graph: triangle area = ½ × 11 × 12 = 66 m, plus rectangle area = 11 × 12 = 132 m. Total distance = 66 + 132 = 198 m.
2. 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 14 s. Calculate the total distance travelled.
204 m
Distance is the area under the speed-time graph: triangle area = ½ × 6 × 12 = 36 m, plus rectangle area = 14 × 12 = 168 m. Total distance = 36 + 168 = 204 m.
3. On a speed-time graph, a train accelerates uniformly from rest to 48 m/s in 6 s and then continues at a constant speed of 48 m/s for a further 13 s. Calculate the total distance travelled.
768 m
Distance is the area under the speed-time graph: triangle area = ½ × 6 × 48 = 144 m, plus rectangle area = 13 × 48 = 624 m. Total distance = 144 + 624 = 768 m.
4. On a speed-time graph, a train accelerates uniformly from rest to 34 m/s in 3 s and then continues at a constant speed of 34 m/s for a further 8 s. Calculate the total distance travelled.
323 m
Distance is the area under the speed-time graph: triangle area = ½ × 3 × 34 = 51 m, plus rectangle area = 8 × 34 = 272 m. Total distance = 51 + 272 = 323 m.
5. On a speed-time graph, a train accelerates uniformly from rest to 40 m/s in 7 s and then continues at a constant speed of 40 m/s for a further 9 s. Calculate the total distance travelled.
500 m
Distance is the area under the speed-time graph: triangle area = ½ × 7 × 40 = 140 m, plus rectangle area = 9 × 40 = 360 m. Total distance = 140 + 360 = 500 m.
6. On a speed-time graph, a train accelerates uniformly from rest to 20 m/s in 9 s and then continues at a constant speed of 20 m/s for a further 14 s. Calculate the total distance travelled.
370 m
Distance is the area under the speed-time graph: triangle area = ½ × 9 × 20 = 90 m, plus rectangle area = 14 × 20 = 280 m. Total distance = 90 + 280 = 370 m.
7. On a speed-time graph, a train accelerates uniformly from rest to 34 m/s in 4 s and then continues at a constant speed of 34 m/s for a further 20 s. Calculate the total distance travelled.
748 m
Distance is the area under the speed-time graph: triangle area = ½ × 4 × 34 = 68 m, plus rectangle area = 20 × 34 = 680 m. Total distance = 68 + 680 = 748 m.
8. On a speed-time graph, a train accelerates uniformly from rest to 34 m/s in 2 s and then continues at a constant speed of 34 m/s for a further 6 s. Calculate the total distance travelled.
238 m
Distance is the area under the speed-time graph: triangle area = ½ × 2 × 34 = 34 m, plus rectangle area = 6 × 34 = 204 m. Total distance = 34 + 204 = 238 m.
9. On a speed-time graph, a train accelerates uniformly from rest to 48 m/s in 12 s and then continues at a constant speed of 48 m/s for a further 4 s. Calculate the total distance travelled.
480 m
Distance is the area under the speed-time graph: triangle area = ½ × 12 × 48 = 288 m, plus rectangle area = 4 × 48 = 192 m. Total distance = 288 + 192 = 480 m.
10. On a speed-time graph, a train accelerates uniformly from rest to 14 m/s in 9 s and then continues at a constant speed of 14 m/s for a further 16 s. Calculate the total distance travelled.
287 m
Distance is the area under the speed-time graph: triangle area = ½ × 9 × 14 = 63 m, plus rectangle area = 16 × 14 = 224 m. Total distance = 63 + 224 = 287 m.
11. 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 12 s. Calculate the total distance travelled.
180 m
Distance is the area under the speed-time graph: triangle area = ½ × 6 × 12 = 36 m, plus rectangle area = 12 × 12 = 144 m. Total distance = 36 + 144 = 180 m.
12. 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 20 s. Calculate the total distance travelled.
1080 m
Distance is the area under the speed-time graph: triangle area = ½ × 5 × 48 = 120 m, plus rectangle area = 20 × 48 = 960 m. Total distance = 120 + 960 = 1080 m.

12 questions · Seed 50 · Age guidance, not curriculum certification