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 28 m/s in 3 s and then continues at a constant speed of 28 m/s for a further 15 s. Calculate the total distance travelled.
v_max = 28 m/s (t₁ = 3 s, t₂ = 15 s) · Distance = Area = ½vt₁ + vt₂
2. On a speed-time graph, a train accelerates uniformly from rest to 30 m/s in 11 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 = 11 s, t₂ = 15 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 12 s. Calculate the total distance travelled.
v_max = 48 m/s (t₁ = 6 s, t₂ = 12 s) · Distance = Area = ½vt₁ + vt₂
4. On a speed-time graph, a train accelerates uniformly from rest to 8 m/s in 4 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 = 4 s, t₂ = 19 s) · Distance = Area = ½vt₁ + vt₂
5. 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 10 s. Calculate the total distance travelled.
v_max = 18 m/s (t₁ = 10 s, t₂ = 10 s) · Distance = Area = ½vt₁ + vt₂
6. 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 17 s. Calculate the total distance travelled.
v_max = 24 m/s (t₁ = 10 s, t₂ = 17 s) · Distance = Area = ½vt₁ + vt₂
7. 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 15 s. Calculate the total distance travelled.
v_max = 20 m/s (t₁ = 9 s, t₂ = 15 s) · Distance = Area = ½vt₁ + vt₂
8. 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 14 s. Calculate the total distance travelled.
v_max = 18 m/s (t₁ = 11 s, t₂ = 14 s) · Distance = Area = ½vt₁ + vt₂
9. On a speed-time graph, a train accelerates uniformly from rest to 8 m/s in 3 s and then continues at a constant speed of 8 m/s for a further 6 s. Calculate the total distance travelled.
v_max = 8 m/s (t₁ = 3 s, t₂ = 6 s) · Distance = Area = ½vt₁ + vt₂
10. 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 6 s. Calculate the total distance travelled.
v_max = 32 m/s (t₁ = 3 s, t₂ = 6 s) · Distance = Area = ½vt₁ + vt₂
11. On a speed-time graph, a train accelerates uniformly from rest to 32 m/s in 10 s and then continues at a constant speed of 32 m/s for a further 6 s. Calculate the total distance travelled.
v_max = 32 m/s (t₁ = 10 s, t₂ = 6 s) · Distance = Area = ½vt₁ + vt₂
12. 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 12 s. Calculate the total distance travelled.
v_max = 8 m/s (t₁ = 6 s, t₂ = 12 s) · Distance = Area = ½vt₁ + vt₂

12 questions · Seed 49 · 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 28 m/s in 3 s and then continues at a constant speed of 28 m/s for a further 15 s. Calculate the total distance travelled.
462 m
Distance is the area under the speed-time graph: triangle area = ½ × 3 × 28 = 42 m, plus rectangle area = 15 × 28 = 420 m. Total distance = 42 + 420 = 462 m.
2. On a speed-time graph, a train accelerates uniformly from rest to 30 m/s in 11 s and then continues at a constant speed of 30 m/s for a further 15 s. Calculate the total distance travelled.
615 m
Distance is the area under the speed-time graph: triangle area = ½ × 11 × 30 = 165 m, plus rectangle area = 15 × 30 = 450 m. Total distance = 165 + 450 = 615 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 12 s. Calculate the total distance travelled.
720 m
Distance is the area under the speed-time graph: triangle area = ½ × 6 × 48 = 144 m, plus rectangle area = 12 × 48 = 576 m. Total distance = 144 + 576 = 720 m.
4. On a speed-time graph, a train accelerates uniformly from rest to 8 m/s in 4 s and then continues at a constant speed of 8 m/s for a further 19 s. Calculate the total distance travelled.
168 m
Distance is the area under the speed-time graph: triangle area = ½ × 4 × 8 = 16 m, plus rectangle area = 19 × 8 = 152 m. Total distance = 16 + 152 = 168 m.
5. 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 10 s. Calculate the total distance travelled.
270 m
Distance is the area under the speed-time graph: triangle area = ½ × 10 × 18 = 90 m, plus rectangle area = 10 × 18 = 180 m. Total distance = 90 + 180 = 270 m.
6. 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 17 s. Calculate the total distance travelled.
528 m
Distance is the area under the speed-time graph: triangle area = ½ × 10 × 24 = 120 m, plus rectangle area = 17 × 24 = 408 m. Total distance = 120 + 408 = 528 m.
7. 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 15 s. Calculate the total distance travelled.
390 m
Distance is the area under the speed-time graph: triangle area = ½ × 9 × 20 = 90 m, plus rectangle area = 15 × 20 = 300 m. Total distance = 90 + 300 = 390 m.
8. 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 14 s. Calculate the total distance travelled.
351 m
Distance is the area under the speed-time graph: triangle area = ½ × 11 × 18 = 99 m, plus rectangle area = 14 × 18 = 252 m. Total distance = 99 + 252 = 351 m.
9. On a speed-time graph, a train accelerates uniformly from rest to 8 m/s in 3 s and then continues at a constant speed of 8 m/s for a further 6 s. Calculate the total distance travelled.
60 m
Distance is the area under the speed-time graph: triangle area = ½ × 3 × 8 = 12 m, plus rectangle area = 6 × 8 = 48 m. Total distance = 12 + 48 = 60 m.
10. 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 6 s. Calculate the total distance travelled.
240 m
Distance is the area under the speed-time graph: triangle area = ½ × 3 × 32 = 48 m, plus rectangle area = 6 × 32 = 192 m. Total distance = 48 + 192 = 240 m.
11. On a speed-time graph, a train accelerates uniformly from rest to 32 m/s in 10 s and then continues at a constant speed of 32 m/s for a further 6 s. Calculate the total distance travelled.
352 m
Distance is the area under the speed-time graph: triangle area = ½ × 10 × 32 = 160 m, plus rectangle area = 6 × 32 = 192 m. Total distance = 160 + 192 = 352 m.
12. 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 12 s. Calculate the total distance travelled.
120 m
Distance is the area under the speed-time graph: triangle area = ½ × 6 × 8 = 24 m, plus rectangle area = 12 × 8 = 96 m. Total distance = 24 + 96 = 120 m.

12 questions · Seed 49 · 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 28 m/s in 3 s and then continues at a constant speed of 28 m/s for a further 15 s. Calculate the total distance travelled.
v_max = 28 m/s (t₁ = 3 s, t₂ = 15 s) · Distance = Area = ½vt₁ + vt₂
2. On a speed-time graph, a train accelerates uniformly from rest to 30 m/s in 11 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 = 11 s, t₂ = 15 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 12 s. Calculate the total distance travelled.
v_max = 48 m/s (t₁ = 6 s, t₂ = 12 s) · Distance = Area = ½vt₁ + vt₂
4. On a speed-time graph, a train accelerates uniformly from rest to 8 m/s in 4 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 = 4 s, t₂ = 19 s) · Distance = Area = ½vt₁ + vt₂
5. 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 10 s. Calculate the total distance travelled.
v_max = 18 m/s (t₁ = 10 s, t₂ = 10 s) · Distance = Area = ½vt₁ + vt₂
6. 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 17 s. Calculate the total distance travelled.
v_max = 24 m/s (t₁ = 10 s, t₂ = 17 s) · Distance = Area = ½vt₁ + vt₂
7. 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 15 s. Calculate the total distance travelled.
v_max = 20 m/s (t₁ = 9 s, t₂ = 15 s) · Distance = Area = ½vt₁ + vt₂
8. 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 14 s. Calculate the total distance travelled.
v_max = 18 m/s (t₁ = 11 s, t₂ = 14 s) · Distance = Area = ½vt₁ + vt₂
9. On a speed-time graph, a train accelerates uniformly from rest to 8 m/s in 3 s and then continues at a constant speed of 8 m/s for a further 6 s. Calculate the total distance travelled.
v_max = 8 m/s (t₁ = 3 s, t₂ = 6 s) · Distance = Area = ½vt₁ + vt₂
10. 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 6 s. Calculate the total distance travelled.
v_max = 32 m/s (t₁ = 3 s, t₂ = 6 s) · Distance = Area = ½vt₁ + vt₂
11. On a speed-time graph, a train accelerates uniformly from rest to 32 m/s in 10 s and then continues at a constant speed of 32 m/s for a further 6 s. Calculate the total distance travelled.
v_max = 32 m/s (t₁ = 10 s, t₂ = 6 s) · Distance = Area = ½vt₁ + vt₂
12. 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 12 s. Calculate the total distance travelled.
v_max = 8 m/s (t₁ = 6 s, t₂ = 12 s) · Distance = Area = ½vt₁ + vt₂

12 questions · Seed 49 · 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 28 m/s in 3 s and then continues at a constant speed of 28 m/s for a further 15 s. Calculate the total distance travelled.
462 m
Distance is the area under the speed-time graph: triangle area = ½ × 3 × 28 = 42 m, plus rectangle area = 15 × 28 = 420 m. Total distance = 42 + 420 = 462 m.
2. On a speed-time graph, a train accelerates uniformly from rest to 30 m/s in 11 s and then continues at a constant speed of 30 m/s for a further 15 s. Calculate the total distance travelled.
615 m
Distance is the area under the speed-time graph: triangle area = ½ × 11 × 30 = 165 m, plus rectangle area = 15 × 30 = 450 m. Total distance = 165 + 450 = 615 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 12 s. Calculate the total distance travelled.
720 m
Distance is the area under the speed-time graph: triangle area = ½ × 6 × 48 = 144 m, plus rectangle area = 12 × 48 = 576 m. Total distance = 144 + 576 = 720 m.
4. On a speed-time graph, a train accelerates uniformly from rest to 8 m/s in 4 s and then continues at a constant speed of 8 m/s for a further 19 s. Calculate the total distance travelled.
168 m
Distance is the area under the speed-time graph: triangle area = ½ × 4 × 8 = 16 m, plus rectangle area = 19 × 8 = 152 m. Total distance = 16 + 152 = 168 m.
5. 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 10 s. Calculate the total distance travelled.
270 m
Distance is the area under the speed-time graph: triangle area = ½ × 10 × 18 = 90 m, plus rectangle area = 10 × 18 = 180 m. Total distance = 90 + 180 = 270 m.
6. 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 17 s. Calculate the total distance travelled.
528 m
Distance is the area under the speed-time graph: triangle area = ½ × 10 × 24 = 120 m, plus rectangle area = 17 × 24 = 408 m. Total distance = 120 + 408 = 528 m.
7. 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 15 s. Calculate the total distance travelled.
390 m
Distance is the area under the speed-time graph: triangle area = ½ × 9 × 20 = 90 m, plus rectangle area = 15 × 20 = 300 m. Total distance = 90 + 300 = 390 m.
8. 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 14 s. Calculate the total distance travelled.
351 m
Distance is the area under the speed-time graph: triangle area = ½ × 11 × 18 = 99 m, plus rectangle area = 14 × 18 = 252 m. Total distance = 99 + 252 = 351 m.
9. On a speed-time graph, a train accelerates uniformly from rest to 8 m/s in 3 s and then continues at a constant speed of 8 m/s for a further 6 s. Calculate the total distance travelled.
60 m
Distance is the area under the speed-time graph: triangle area = ½ × 3 × 8 = 12 m, plus rectangle area = 6 × 8 = 48 m. Total distance = 12 + 48 = 60 m.
10. 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 6 s. Calculate the total distance travelled.
240 m
Distance is the area under the speed-time graph: triangle area = ½ × 3 × 32 = 48 m, plus rectangle area = 6 × 32 = 192 m. Total distance = 48 + 192 = 240 m.
11. On a speed-time graph, a train accelerates uniformly from rest to 32 m/s in 10 s and then continues at a constant speed of 32 m/s for a further 6 s. Calculate the total distance travelled.
352 m
Distance is the area under the speed-time graph: triangle area = ½ × 10 × 32 = 160 m, plus rectangle area = 6 × 32 = 192 m. Total distance = 160 + 192 = 352 m.
12. 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 12 s. Calculate the total distance travelled.
120 m
Distance is the area under the speed-time graph: triangle area = ½ × 6 × 8 = 24 m, plus rectangle area = 12 × 8 = 96 m. Total distance = 24 + 96 = 120 m.

12 questions · Seed 49 · Age guidance, not curriculum certification