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 10 m/s in 12 s and then continues at a constant speed of 10 m/s for a further 20 s. Calculate the total distance travelled.
v_max = 10 m/s (t₁ = 12 s, t₂ = 20 s) · Distance = Area = ½vt₁ + vt₂
2. On a speed-time graph, a train accelerates uniformly from rest to 20 m/s in 11 s and then continues at a constant speed of 20 m/s for a further 17 s. Calculate the total distance travelled.
v_max = 20 m/s (t₁ = 11 s, t₂ = 17 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 10 s. Calculate the total distance travelled.
v_max = 44 m/s (t₁ = 12 s, t₂ = 10 s) · Distance = Area = ½vt₁ + vt₂
4. On a speed-time graph, a train accelerates uniformly from rest to 8 m/s in 9 s and then continues at a constant speed of 8 m/s for a further 10 s. Calculate the total distance travelled.
v_max = 8 m/s (t₁ = 9 s, t₂ = 10 s) · Distance = Area = ½vt₁ + vt₂
5. On a speed-time graph, a train accelerates uniformly from rest to 38 m/s in 2 s and then continues at a constant speed of 38 m/s for a further 6 s. Calculate the total distance travelled.
v_max = 38 m/s (t₁ = 2 s, t₂ = 6 s) · Distance = Area = ½vt₁ + vt₂
6. 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 16 s. Calculate the total distance travelled.
v_max = 8 m/s (t₁ = 6 s, t₂ = 16 s) · Distance = Area = ½vt₁ + vt₂
7. 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 11 s. Calculate the total distance travelled.
v_max = 46 m/s (t₁ = 9 s, t₂ = 11 s) · Distance = Area = ½vt₁ + vt₂
8. On a speed-time graph, a train accelerates uniformly from rest to 30 m/s in 8 s and then continues at a constant speed of 30 m/s for a further 5 s. Calculate the total distance travelled.
v_max = 30 m/s (t₁ = 8 s, t₂ = 5 s) · Distance = Area = ½vt₁ + vt₂
9. On a speed-time graph, a train accelerates uniformly from rest to 32 m/s in 3 s and then continues at a constant speed of 32 m/s for a further 18 s. Calculate the total distance travelled.
v_max = 32 m/s (t₁ = 3 s, t₂ = 18 s) · Distance = Area = ½vt₁ + vt₂
10. 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 20 s. Calculate the total distance travelled.
v_max = 36 m/s (t₁ = 8 s, t₂ = 20 s) · Distance = Area = ½vt₁ + vt₂
11. On a speed-time graph, a train accelerates uniformly from rest to 8 m/s in 11 s and then continues at a constant speed of 8 m/s for a further 19 s. Calculate the total distance travelled.
v_max = 8 m/s (t₁ = 11 s, t₂ = 19 s) · Distance = Area = ½vt₁ + vt₂
12. 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 8 s. Calculate the total distance travelled.
v_max = 48 m/s (t₁ = 10 s, t₂ = 8 s) · Distance = Area = ½vt₁ + vt₂

12 questions · Seed 44 · 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 10 m/s in 12 s and then continues at a constant speed of 10 m/s for a further 20 s. Calculate the total distance travelled.
260 m
Distance is the area under the speed-time graph: triangle area = ½ × 12 × 10 = 60 m, plus rectangle area = 20 × 10 = 200 m. Total distance = 60 + 200 = 260 m.
2. On a speed-time graph, a train accelerates uniformly from rest to 20 m/s in 11 s and then continues at a constant speed of 20 m/s for a further 17 s. Calculate the total distance travelled.
450 m
Distance is the area under the speed-time graph: triangle area = ½ × 11 × 20 = 110 m, plus rectangle area = 17 × 20 = 340 m. Total distance = 110 + 340 = 450 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 10 s. Calculate the total distance travelled.
704 m
Distance is the area under the speed-time graph: triangle area = ½ × 12 × 44 = 264 m, plus rectangle area = 10 × 44 = 440 m. Total distance = 264 + 440 = 704 m.
4. On a speed-time graph, a train accelerates uniformly from rest to 8 m/s in 9 s and then continues at a constant speed of 8 m/s for a further 10 s. Calculate the total distance travelled.
116 m
Distance is the area under the speed-time graph: triangle area = ½ × 9 × 8 = 36 m, plus rectangle area = 10 × 8 = 80 m. Total distance = 36 + 80 = 116 m.
5. On a speed-time graph, a train accelerates uniformly from rest to 38 m/s in 2 s and then continues at a constant speed of 38 m/s for a further 6 s. Calculate the total distance travelled.
266 m
Distance is the area under the speed-time graph: triangle area = ½ × 2 × 38 = 38 m, plus rectangle area = 6 × 38 = 228 m. Total distance = 38 + 228 = 266 m.
6. 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 16 s. Calculate the total distance travelled.
152 m
Distance is the area under the speed-time graph: triangle area = ½ × 6 × 8 = 24 m, plus rectangle area = 16 × 8 = 128 m. Total distance = 24 + 128 = 152 m.
7. 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 11 s. Calculate the total distance travelled.
713 m
Distance is the area under the speed-time graph: triangle area = ½ × 9 × 46 = 207 m, plus rectangle area = 11 × 46 = 506 m. Total distance = 207 + 506 = 713 m.
8. On a speed-time graph, a train accelerates uniformly from rest to 30 m/s in 8 s and then continues at a constant speed of 30 m/s for a further 5 s. Calculate the total distance travelled.
270 m
Distance is the area under the speed-time graph: triangle area = ½ × 8 × 30 = 120 m, plus rectangle area = 5 × 30 = 150 m. Total distance = 120 + 150 = 270 m.
9. On a speed-time graph, a train accelerates uniformly from rest to 32 m/s in 3 s and then continues at a constant speed of 32 m/s for a further 18 s. Calculate the total distance travelled.
624 m
Distance is the area under the speed-time graph: triangle area = ½ × 3 × 32 = 48 m, plus rectangle area = 18 × 32 = 576 m. Total distance = 48 + 576 = 624 m.
10. 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 20 s. Calculate the total distance travelled.
864 m
Distance is the area under the speed-time graph: triangle area = ½ × 8 × 36 = 144 m, plus rectangle area = 20 × 36 = 720 m. Total distance = 144 + 720 = 864 m.
11. On a speed-time graph, a train accelerates uniformly from rest to 8 m/s in 11 s and then continues at a constant speed of 8 m/s for a further 19 s. Calculate the total distance travelled.
196 m
Distance is the area under the speed-time graph: triangle area = ½ × 11 × 8 = 44 m, plus rectangle area = 19 × 8 = 152 m. Total distance = 44 + 152 = 196 m.
12. 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 8 s. Calculate the total distance travelled.
624 m
Distance is the area under the speed-time graph: triangle area = ½ × 10 × 48 = 240 m, plus rectangle area = 8 × 48 = 384 m. Total distance = 240 + 384 = 624 m.

12 questions · Seed 44 · 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 10 m/s in 12 s and then continues at a constant speed of 10 m/s for a further 20 s. Calculate the total distance travelled.
v_max = 10 m/s (t₁ = 12 s, t₂ = 20 s) · Distance = Area = ½vt₁ + vt₂
2. On a speed-time graph, a train accelerates uniformly from rest to 20 m/s in 11 s and then continues at a constant speed of 20 m/s for a further 17 s. Calculate the total distance travelled.
v_max = 20 m/s (t₁ = 11 s, t₂ = 17 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 10 s. Calculate the total distance travelled.
v_max = 44 m/s (t₁ = 12 s, t₂ = 10 s) · Distance = Area = ½vt₁ + vt₂
4. On a speed-time graph, a train accelerates uniformly from rest to 8 m/s in 9 s and then continues at a constant speed of 8 m/s for a further 10 s. Calculate the total distance travelled.
v_max = 8 m/s (t₁ = 9 s, t₂ = 10 s) · Distance = Area = ½vt₁ + vt₂
5. On a speed-time graph, a train accelerates uniformly from rest to 38 m/s in 2 s and then continues at a constant speed of 38 m/s for a further 6 s. Calculate the total distance travelled.
v_max = 38 m/s (t₁ = 2 s, t₂ = 6 s) · Distance = Area = ½vt₁ + vt₂
6. 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 16 s. Calculate the total distance travelled.
v_max = 8 m/s (t₁ = 6 s, t₂ = 16 s) · Distance = Area = ½vt₁ + vt₂
7. 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 11 s. Calculate the total distance travelled.
v_max = 46 m/s (t₁ = 9 s, t₂ = 11 s) · Distance = Area = ½vt₁ + vt₂
8. On a speed-time graph, a train accelerates uniformly from rest to 30 m/s in 8 s and then continues at a constant speed of 30 m/s for a further 5 s. Calculate the total distance travelled.
v_max = 30 m/s (t₁ = 8 s, t₂ = 5 s) · Distance = Area = ½vt₁ + vt₂
9. On a speed-time graph, a train accelerates uniformly from rest to 32 m/s in 3 s and then continues at a constant speed of 32 m/s for a further 18 s. Calculate the total distance travelled.
v_max = 32 m/s (t₁ = 3 s, t₂ = 18 s) · Distance = Area = ½vt₁ + vt₂
10. 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 20 s. Calculate the total distance travelled.
v_max = 36 m/s (t₁ = 8 s, t₂ = 20 s) · Distance = Area = ½vt₁ + vt₂
11. On a speed-time graph, a train accelerates uniformly from rest to 8 m/s in 11 s and then continues at a constant speed of 8 m/s for a further 19 s. Calculate the total distance travelled.
v_max = 8 m/s (t₁ = 11 s, t₂ = 19 s) · Distance = Area = ½vt₁ + vt₂
12. 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 8 s. Calculate the total distance travelled.
v_max = 48 m/s (t₁ = 10 s, t₂ = 8 s) · Distance = Area = ½vt₁ + vt₂

12 questions · Seed 44 · 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 10 m/s in 12 s and then continues at a constant speed of 10 m/s for a further 20 s. Calculate the total distance travelled.
260 m
Distance is the area under the speed-time graph: triangle area = ½ × 12 × 10 = 60 m, plus rectangle area = 20 × 10 = 200 m. Total distance = 60 + 200 = 260 m.
2. On a speed-time graph, a train accelerates uniformly from rest to 20 m/s in 11 s and then continues at a constant speed of 20 m/s for a further 17 s. Calculate the total distance travelled.
450 m
Distance is the area under the speed-time graph: triangle area = ½ × 11 × 20 = 110 m, plus rectangle area = 17 × 20 = 340 m. Total distance = 110 + 340 = 450 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 10 s. Calculate the total distance travelled.
704 m
Distance is the area under the speed-time graph: triangle area = ½ × 12 × 44 = 264 m, plus rectangle area = 10 × 44 = 440 m. Total distance = 264 + 440 = 704 m.
4. On a speed-time graph, a train accelerates uniformly from rest to 8 m/s in 9 s and then continues at a constant speed of 8 m/s for a further 10 s. Calculate the total distance travelled.
116 m
Distance is the area under the speed-time graph: triangle area = ½ × 9 × 8 = 36 m, plus rectangle area = 10 × 8 = 80 m. Total distance = 36 + 80 = 116 m.
5. On a speed-time graph, a train accelerates uniformly from rest to 38 m/s in 2 s and then continues at a constant speed of 38 m/s for a further 6 s. Calculate the total distance travelled.
266 m
Distance is the area under the speed-time graph: triangle area = ½ × 2 × 38 = 38 m, plus rectangle area = 6 × 38 = 228 m. Total distance = 38 + 228 = 266 m.
6. 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 16 s. Calculate the total distance travelled.
152 m
Distance is the area under the speed-time graph: triangle area = ½ × 6 × 8 = 24 m, plus rectangle area = 16 × 8 = 128 m. Total distance = 24 + 128 = 152 m.
7. 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 11 s. Calculate the total distance travelled.
713 m
Distance is the area under the speed-time graph: triangle area = ½ × 9 × 46 = 207 m, plus rectangle area = 11 × 46 = 506 m. Total distance = 207 + 506 = 713 m.
8. On a speed-time graph, a train accelerates uniformly from rest to 30 m/s in 8 s and then continues at a constant speed of 30 m/s for a further 5 s. Calculate the total distance travelled.
270 m
Distance is the area under the speed-time graph: triangle area = ½ × 8 × 30 = 120 m, plus rectangle area = 5 × 30 = 150 m. Total distance = 120 + 150 = 270 m.
9. On a speed-time graph, a train accelerates uniformly from rest to 32 m/s in 3 s and then continues at a constant speed of 32 m/s for a further 18 s. Calculate the total distance travelled.
624 m
Distance is the area under the speed-time graph: triangle area = ½ × 3 × 32 = 48 m, plus rectangle area = 18 × 32 = 576 m. Total distance = 48 + 576 = 624 m.
10. 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 20 s. Calculate the total distance travelled.
864 m
Distance is the area under the speed-time graph: triangle area = ½ × 8 × 36 = 144 m, plus rectangle area = 20 × 36 = 720 m. Total distance = 144 + 720 = 864 m.
11. On a speed-time graph, a train accelerates uniformly from rest to 8 m/s in 11 s and then continues at a constant speed of 8 m/s for a further 19 s. Calculate the total distance travelled.
196 m
Distance is the area under the speed-time graph: triangle area = ½ × 11 × 8 = 44 m, plus rectangle area = 19 × 8 = 152 m. Total distance = 44 + 152 = 196 m.
12. 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 8 s. Calculate the total distance travelled.
624 m
Distance is the area under the speed-time graph: triangle area = ½ × 10 × 48 = 240 m, plus rectangle area = 8 × 48 = 384 m. Total distance = 240 + 384 = 624 m.

12 questions · Seed 44 · Age guidance, not curriculum certification