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 38 m/s in 10 s and then continues at a constant speed of 38 m/s for a further 16 s. Calculate the total distance travelled.
v_max = 38 m/s (t₁ = 10 s, t₂ = 16 s) · Distance = Area = ½vt₁ + vt₂
2. On a speed-time graph, a train accelerates uniformly from rest to 44 m/s in 5 s and then continues at a constant speed of 44 m/s for a further 15 s. Calculate the total distance travelled.
v_max = 44 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 44 m/s in 12 s and then continues at a constant speed of 44 m/s for a further 12 s. Calculate the total distance travelled.
v_max = 44 m/s (t₁ = 12 s, t₂ = 12 s) · Distance = Area = ½vt₁ + vt₂
4. On a speed-time graph, a train accelerates uniformly from rest to 34 m/s in 9 s and then continues at a constant speed of 34 m/s for a further 17 s. Calculate the total distance travelled.
v_max = 34 m/s (t₁ = 9 s, t₂ = 17 s) · Distance = Area = ½vt₁ + vt₂
5. On a speed-time graph, a train accelerates uniformly from rest to 16 m/s in 10 s and then continues at a constant speed of 16 m/s for a further 5 s. Calculate the total distance travelled.
v_max = 16 m/s (t₁ = 10 s, t₂ = 5 s) · Distance = Area = ½vt₁ + vt₂
6. 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
7. 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 15 s. Calculate the total distance travelled.
v_max = 16 m/s (t₁ = 4 s, t₂ = 15 s) · Distance = Area = ½vt₁ + vt₂
8. 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 14 s. Calculate the total distance travelled.
v_max = 46 m/s (t₁ = 9 s, t₂ = 14 s) · Distance = Area = ½vt₁ + vt₂
9. On a speed-time graph, a train accelerates uniformly from rest to 26 m/s in 11 s and then continues at a constant speed of 26 m/s for a further 16 s. Calculate the total distance travelled.
v_max = 26 m/s (t₁ = 11 s, t₂ = 16 s) · Distance = Area = ½vt₁ + vt₂
10. 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 13 s. Calculate the total distance travelled.
v_max = 18 m/s (t₁ = 4 s, t₂ = 13 s) · Distance = Area = ½vt₁ + vt₂
11. On a speed-time graph, a train accelerates uniformly from rest to 32 m/s in 7 s and then continues at a constant speed of 32 m/s for a further 8 s. Calculate the total distance travelled.
v_max = 32 m/s (t₁ = 7 s, t₂ = 8 s) · Distance = Area = ½vt₁ + vt₂
12. On a speed-time graph, a train accelerates uniformly from rest to 44 m/s in 10 s and then continues at a constant speed of 44 m/s for a further 16 s. Calculate the total distance travelled.
v_max = 44 m/s (t₁ = 10 s, t₂ = 16 s) · Distance = Area = ½vt₁ + vt₂

12 questions · Seed 45 · Age guidance, not curriculum certification

View the answer key

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 38 m/s in 10 s and then continues at a constant speed of 38 m/s for a further 16 s. Calculate the total distance travelled.
798 m
Distance is the area under the speed-time graph: triangle area = ½ × 10 × 38 = 190 m, plus rectangle area = 16 × 38 = 608 m. Total distance = 190 + 608 = 798 m.
2. On a speed-time graph, a train accelerates uniformly from rest to 44 m/s in 5 s and then continues at a constant speed of 44 m/s for a further 15 s. Calculate the total distance travelled.
770 m
Distance is the area under the speed-time graph: triangle area = ½ × 5 × 44 = 110 m, plus rectangle area = 15 × 44 = 660 m. Total distance = 110 + 660 = 770 m.
3. On a speed-time graph, a train accelerates uniformly from rest to 44 m/s in 12 s and then continues at a constant speed of 44 m/s for a further 12 s. Calculate the total distance travelled.
792 m
Distance is the area under the speed-time graph: triangle area = ½ × 12 × 44 = 264 m, plus rectangle area = 12 × 44 = 528 m. Total distance = 264 + 528 = 792 m.
4. On a speed-time graph, a train accelerates uniformly from rest to 34 m/s in 9 s and then continues at a constant speed of 34 m/s for a further 17 s. Calculate the total distance travelled.
731 m
Distance is the area under the speed-time graph: triangle area = ½ × 9 × 34 = 153 m, plus rectangle area = 17 × 34 = 578 m. Total distance = 153 + 578 = 731 m.
5. On a speed-time graph, a train accelerates uniformly from rest to 16 m/s in 10 s and then continues at a constant speed of 16 m/s for a further 5 s. Calculate the total distance travelled.
160 m
Distance is the area under the speed-time graph: triangle area = ½ × 10 × 16 = 80 m, plus rectangle area = 5 × 16 = 80 m. Total distance = 80 + 80 = 160 m.
6. 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.
7. 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 15 s. Calculate the total distance travelled.
272 m
Distance is the area under the speed-time graph: triangle area = ½ × 4 × 16 = 32 m, plus rectangle area = 15 × 16 = 240 m. Total distance = 32 + 240 = 272 m.
8. 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 14 s. Calculate the total distance travelled.
851 m
Distance is the area under the speed-time graph: triangle area = ½ × 9 × 46 = 207 m, plus rectangle area = 14 × 46 = 644 m. Total distance = 207 + 644 = 851 m.
9. On a speed-time graph, a train accelerates uniformly from rest to 26 m/s in 11 s and then continues at a constant speed of 26 m/s for a further 16 s. Calculate the total distance travelled.
559 m
Distance is the area under the speed-time graph: triangle area = ½ × 11 × 26 = 143 m, plus rectangle area = 16 × 26 = 416 m. Total distance = 143 + 416 = 559 m.
10. 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 13 s. Calculate the total distance travelled.
270 m
Distance is the area under the speed-time graph: triangle area = ½ × 4 × 18 = 36 m, plus rectangle area = 13 × 18 = 234 m. Total distance = 36 + 234 = 270 m.
11. On a speed-time graph, a train accelerates uniformly from rest to 32 m/s in 7 s and then continues at a constant speed of 32 m/s for a further 8 s. Calculate the total distance travelled.
368 m
Distance is the area under the speed-time graph: triangle area = ½ × 7 × 32 = 112 m, plus rectangle area = 8 × 32 = 256 m. Total distance = 112 + 256 = 368 m.
12. On a speed-time graph, a train accelerates uniformly from rest to 44 m/s in 10 s and then continues at a constant speed of 44 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 × 10 × 44 = 220 m, plus rectangle area = 16 × 44 = 704 m. Total distance = 220 + 704 = 924 m.

12 questions · Seed 45 · 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 38 m/s in 10 s and then continues at a constant speed of 38 m/s for a further 16 s. Calculate the total distance travelled.
v_max = 38 m/s (t₁ = 10 s, t₂ = 16 s) · Distance = Area = ½vt₁ + vt₂
2. On a speed-time graph, a train accelerates uniformly from rest to 44 m/s in 5 s and then continues at a constant speed of 44 m/s for a further 15 s. Calculate the total distance travelled.
v_max = 44 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 44 m/s in 12 s and then continues at a constant speed of 44 m/s for a further 12 s. Calculate the total distance travelled.
v_max = 44 m/s (t₁ = 12 s, t₂ = 12 s) · Distance = Area = ½vt₁ + vt₂
4. On a speed-time graph, a train accelerates uniformly from rest to 34 m/s in 9 s and then continues at a constant speed of 34 m/s for a further 17 s. Calculate the total distance travelled.
v_max = 34 m/s (t₁ = 9 s, t₂ = 17 s) · Distance = Area = ½vt₁ + vt₂
5. On a speed-time graph, a train accelerates uniformly from rest to 16 m/s in 10 s and then continues at a constant speed of 16 m/s for a further 5 s. Calculate the total distance travelled.
v_max = 16 m/s (t₁ = 10 s, t₂ = 5 s) · Distance = Area = ½vt₁ + vt₂
6. 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
7. 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 15 s. Calculate the total distance travelled.
v_max = 16 m/s (t₁ = 4 s, t₂ = 15 s) · Distance = Area = ½vt₁ + vt₂
8. 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 14 s. Calculate the total distance travelled.
v_max = 46 m/s (t₁ = 9 s, t₂ = 14 s) · Distance = Area = ½vt₁ + vt₂
9. On a speed-time graph, a train accelerates uniformly from rest to 26 m/s in 11 s and then continues at a constant speed of 26 m/s for a further 16 s. Calculate the total distance travelled.
v_max = 26 m/s (t₁ = 11 s, t₂ = 16 s) · Distance = Area = ½vt₁ + vt₂
10. 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 13 s. Calculate the total distance travelled.
v_max = 18 m/s (t₁ = 4 s, t₂ = 13 s) · Distance = Area = ½vt₁ + vt₂
11. On a speed-time graph, a train accelerates uniformly from rest to 32 m/s in 7 s and then continues at a constant speed of 32 m/s for a further 8 s. Calculate the total distance travelled.
v_max = 32 m/s (t₁ = 7 s, t₂ = 8 s) · Distance = Area = ½vt₁ + vt₂
12. On a speed-time graph, a train accelerates uniformly from rest to 44 m/s in 10 s and then continues at a constant speed of 44 m/s for a further 16 s. Calculate the total distance travelled.
v_max = 44 m/s (t₁ = 10 s, t₂ = 16 s) · Distance = Area = ½vt₁ + vt₂

12 questions · Seed 45 · 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 38 m/s in 10 s and then continues at a constant speed of 38 m/s for a further 16 s. Calculate the total distance travelled.
798 m
Distance is the area under the speed-time graph: triangle area = ½ × 10 × 38 = 190 m, plus rectangle area = 16 × 38 = 608 m. Total distance = 190 + 608 = 798 m.
2. On a speed-time graph, a train accelerates uniformly from rest to 44 m/s in 5 s and then continues at a constant speed of 44 m/s for a further 15 s. Calculate the total distance travelled.
770 m
Distance is the area under the speed-time graph: triangle area = ½ × 5 × 44 = 110 m, plus rectangle area = 15 × 44 = 660 m. Total distance = 110 + 660 = 770 m.
3. On a speed-time graph, a train accelerates uniformly from rest to 44 m/s in 12 s and then continues at a constant speed of 44 m/s for a further 12 s. Calculate the total distance travelled.
792 m
Distance is the area under the speed-time graph: triangle area = ½ × 12 × 44 = 264 m, plus rectangle area = 12 × 44 = 528 m. Total distance = 264 + 528 = 792 m.
4. On a speed-time graph, a train accelerates uniformly from rest to 34 m/s in 9 s and then continues at a constant speed of 34 m/s for a further 17 s. Calculate the total distance travelled.
731 m
Distance is the area under the speed-time graph: triangle area = ½ × 9 × 34 = 153 m, plus rectangle area = 17 × 34 = 578 m. Total distance = 153 + 578 = 731 m.
5. On a speed-time graph, a train accelerates uniformly from rest to 16 m/s in 10 s and then continues at a constant speed of 16 m/s for a further 5 s. Calculate the total distance travelled.
160 m
Distance is the area under the speed-time graph: triangle area = ½ × 10 × 16 = 80 m, plus rectangle area = 5 × 16 = 80 m. Total distance = 80 + 80 = 160 m.
6. 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.
7. 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 15 s. Calculate the total distance travelled.
272 m
Distance is the area under the speed-time graph: triangle area = ½ × 4 × 16 = 32 m, plus rectangle area = 15 × 16 = 240 m. Total distance = 32 + 240 = 272 m.
8. 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 14 s. Calculate the total distance travelled.
851 m
Distance is the area under the speed-time graph: triangle area = ½ × 9 × 46 = 207 m, plus rectangle area = 14 × 46 = 644 m. Total distance = 207 + 644 = 851 m.
9. On a speed-time graph, a train accelerates uniformly from rest to 26 m/s in 11 s and then continues at a constant speed of 26 m/s for a further 16 s. Calculate the total distance travelled.
559 m
Distance is the area under the speed-time graph: triangle area = ½ × 11 × 26 = 143 m, plus rectangle area = 16 × 26 = 416 m. Total distance = 143 + 416 = 559 m.
10. 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 13 s. Calculate the total distance travelled.
270 m
Distance is the area under the speed-time graph: triangle area = ½ × 4 × 18 = 36 m, plus rectangle area = 13 × 18 = 234 m. Total distance = 36 + 234 = 270 m.
11. On a speed-time graph, a train accelerates uniformly from rest to 32 m/s in 7 s and then continues at a constant speed of 32 m/s for a further 8 s. Calculate the total distance travelled.
368 m
Distance is the area under the speed-time graph: triangle area = ½ × 7 × 32 = 112 m, plus rectangle area = 8 × 32 = 256 m. Total distance = 112 + 256 = 368 m.
12. On a speed-time graph, a train accelerates uniformly from rest to 44 m/s in 10 s and then continues at a constant speed of 44 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 × 10 × 44 = 220 m, plus rectangle area = 16 × 44 = 704 m. Total distance = 220 + 704 = 924 m.

12 questions · Seed 45 · Age guidance, not curriculum certification