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 16 m/s in 9 s and then continues at a constant speed of 16 m/s for a further 9 s. Calculate the total distance travelled.
v_max = 16 m/s (t₁ = 9 s, t₂ = 9 s) · Distance = Area = ½vt₁ + vt₂
2. 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 12 s. Calculate the total distance travelled.
v_max = 16 m/s (t₁ = 10 s, t₂ = 12 s) · Distance = Area = ½vt₁ + vt₂
3. 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 12 s. Calculate the total distance travelled.
v_max = 30 m/s (t₁ = 8 s, t₂ = 12 s) · Distance = Area = ½vt₁ + vt₂
4. On a speed-time graph, a train accelerates uniformly from rest to 18 m/s in 6 s and then continues at a constant speed of 18 m/s for a further 16 s. Calculate the total distance travelled.
v_max = 18 m/s (t₁ = 6 s, t₂ = 16 s) · Distance = Area = ½vt₁ + vt₂
5. On a speed-time graph, a train accelerates uniformly from rest to 14 m/s in 5 s and then continues at a constant speed of 14 m/s for a further 15 s. Calculate the total distance travelled.
v_max = 14 m/s (t₁ = 5 s, t₂ = 15 s) · Distance = Area = ½vt₁ + vt₂
6. On a speed-time graph, a train accelerates uniformly from rest to 10 m/s in 9 s and then continues at a constant speed of 10 m/s for a further 6 s. Calculate the total distance travelled.
v_max = 10 m/s (t₁ = 9 s, t₂ = 6 s) · Distance = Area = ½vt₁ + vt₂
7. On a speed-time graph, a train accelerates uniformly from rest to 18 m/s in 3 s and then continues at a constant speed of 18 m/s for a further 16 s. Calculate the total distance travelled.
v_max = 18 m/s (t₁ = 3 s, t₂ = 16 s) · Distance = Area = ½vt₁ + vt₂
8. On a speed-time graph, a train accelerates uniformly from rest to 8 m/s in 2 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 = 2 s, t₂ = 16 s) · Distance = Area = ½vt₁ + vt₂
9. 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 17 s. Calculate the total distance travelled.
v_max = 30 m/s (t₁ = 8 s, t₂ = 17 s) · Distance = Area = ½vt₁ + vt₂
10. On a speed-time graph, a train accelerates uniformly from rest to 34 m/s in 5 s and then continues at a constant speed of 34 m/s for a further 4 s. Calculate the total distance travelled.
v_max = 34 m/s (t₁ = 5 s, t₂ = 4 s) · Distance = Area = ½vt₁ + vt₂
11. On a speed-time graph, a train accelerates uniformly from rest to 18 m/s in 6 s and then continues at a constant speed of 18 m/s for a further 4 s. Calculate the total distance travelled.
v_max = 18 m/s (t₁ = 6 s, t₂ = 4 s) · Distance = Area = ½vt₁ + vt₂
12. 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 15 s. Calculate the total distance travelled.
v_max = 18 m/s (t₁ = 10 s, t₂ = 15 s) · Distance = Area = ½vt₁ + vt₂

12 questions · Seed 104736 · 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 16 m/s in 9 s and then continues at a constant speed of 16 m/s for a further 9 s. Calculate the total distance travelled.
216 m
Distance is the area under the speed-time graph: triangle area = ½ × 9 × 16 = 72 m, plus rectangle area = 9 × 16 = 144 m. Total distance = 72 + 144 = 216 m.
2. 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 12 s. Calculate the total distance travelled.
272 m
Distance is the area under the speed-time graph: triangle area = ½ × 10 × 16 = 80 m, plus rectangle area = 12 × 16 = 192 m. Total distance = 80 + 192 = 272 m.
3. 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 12 s. Calculate the total distance travelled.
480 m
Distance is the area under the speed-time graph: triangle area = ½ × 8 × 30 = 120 m, plus rectangle area = 12 × 30 = 360 m. Total distance = 120 + 360 = 480 m.
4. On a speed-time graph, a train accelerates uniformly from rest to 18 m/s in 6 s and then continues at a constant speed of 18 m/s for a further 16 s. Calculate the total distance travelled.
342 m
Distance is the area under the speed-time graph: triangle area = ½ × 6 × 18 = 54 m, plus rectangle area = 16 × 18 = 288 m. Total distance = 54 + 288 = 342 m.
5. On a speed-time graph, a train accelerates uniformly from rest to 14 m/s in 5 s and then continues at a constant speed of 14 m/s for a further 15 s. Calculate the total distance travelled.
245 m
Distance is the area under the speed-time graph: triangle area = ½ × 5 × 14 = 35 m, plus rectangle area = 15 × 14 = 210 m. Total distance = 35 + 210 = 245 m.
6. On a speed-time graph, a train accelerates uniformly from rest to 10 m/s in 9 s and then continues at a constant speed of 10 m/s for a further 6 s. Calculate the total distance travelled.
105 m
Distance is the area under the speed-time graph: triangle area = ½ × 9 × 10 = 45 m, plus rectangle area = 6 × 10 = 60 m. Total distance = 45 + 60 = 105 m.
7. On a speed-time graph, a train accelerates uniformly from rest to 18 m/s in 3 s and then continues at a constant speed of 18 m/s for a further 16 s. Calculate the total distance travelled.
315 m
Distance is the area under the speed-time graph: triangle area = ½ × 3 × 18 = 27 m, plus rectangle area = 16 × 18 = 288 m. Total distance = 27 + 288 = 315 m.
8. On a speed-time graph, a train accelerates uniformly from rest to 8 m/s in 2 s and then continues at a constant speed of 8 m/s for a further 16 s. Calculate the total distance travelled.
136 m
Distance is the area under the speed-time graph: triangle area = ½ × 2 × 8 = 8 m, plus rectangle area = 16 × 8 = 128 m. Total distance = 8 + 128 = 136 m.
9. 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 17 s. Calculate the total distance travelled.
630 m
Distance is the area under the speed-time graph: triangle area = ½ × 8 × 30 = 120 m, plus rectangle area = 17 × 30 = 510 m. Total distance = 120 + 510 = 630 m.
10. On a speed-time graph, a train accelerates uniformly from rest to 34 m/s in 5 s and then continues at a constant speed of 34 m/s for a further 4 s. Calculate the total distance travelled.
221 m
Distance is the area under the speed-time graph: triangle area = ½ × 5 × 34 = 85 m, plus rectangle area = 4 × 34 = 136 m. Total distance = 85 + 136 = 221 m.
11. On a speed-time graph, a train accelerates uniformly from rest to 18 m/s in 6 s and then continues at a constant speed of 18 m/s for a further 4 s. Calculate the total distance travelled.
126 m
Distance is the area under the speed-time graph: triangle area = ½ × 6 × 18 = 54 m, plus rectangle area = 4 × 18 = 72 m. Total distance = 54 + 72 = 126 m.
12. 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 15 s. Calculate the total distance travelled.
360 m
Distance is the area under the speed-time graph: triangle area = ½ × 10 × 18 = 90 m, plus rectangle area = 15 × 18 = 270 m. Total distance = 90 + 270 = 360 m.

12 questions · Seed 104736 · 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 16 m/s in 9 s and then continues at a constant speed of 16 m/s for a further 9 s. Calculate the total distance travelled.
v_max = 16 m/s (t₁ = 9 s, t₂ = 9 s) · Distance = Area = ½vt₁ + vt₂
2. 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 12 s. Calculate the total distance travelled.
v_max = 16 m/s (t₁ = 10 s, t₂ = 12 s) · Distance = Area = ½vt₁ + vt₂
3. 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 12 s. Calculate the total distance travelled.
v_max = 30 m/s (t₁ = 8 s, t₂ = 12 s) · Distance = Area = ½vt₁ + vt₂
4. On a speed-time graph, a train accelerates uniformly from rest to 18 m/s in 6 s and then continues at a constant speed of 18 m/s for a further 16 s. Calculate the total distance travelled.
v_max = 18 m/s (t₁ = 6 s, t₂ = 16 s) · Distance = Area = ½vt₁ + vt₂
5. On a speed-time graph, a train accelerates uniformly from rest to 14 m/s in 5 s and then continues at a constant speed of 14 m/s for a further 15 s. Calculate the total distance travelled.
v_max = 14 m/s (t₁ = 5 s, t₂ = 15 s) · Distance = Area = ½vt₁ + vt₂
6. On a speed-time graph, a train accelerates uniformly from rest to 10 m/s in 9 s and then continues at a constant speed of 10 m/s for a further 6 s. Calculate the total distance travelled.
v_max = 10 m/s (t₁ = 9 s, t₂ = 6 s) · Distance = Area = ½vt₁ + vt₂
7. On a speed-time graph, a train accelerates uniformly from rest to 18 m/s in 3 s and then continues at a constant speed of 18 m/s for a further 16 s. Calculate the total distance travelled.
v_max = 18 m/s (t₁ = 3 s, t₂ = 16 s) · Distance = Area = ½vt₁ + vt₂
8. On a speed-time graph, a train accelerates uniformly from rest to 8 m/s in 2 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 = 2 s, t₂ = 16 s) · Distance = Area = ½vt₁ + vt₂
9. 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 17 s. Calculate the total distance travelled.
v_max = 30 m/s (t₁ = 8 s, t₂ = 17 s) · Distance = Area = ½vt₁ + vt₂
10. On a speed-time graph, a train accelerates uniformly from rest to 34 m/s in 5 s and then continues at a constant speed of 34 m/s for a further 4 s. Calculate the total distance travelled.
v_max = 34 m/s (t₁ = 5 s, t₂ = 4 s) · Distance = Area = ½vt₁ + vt₂
11. On a speed-time graph, a train accelerates uniformly from rest to 18 m/s in 6 s and then continues at a constant speed of 18 m/s for a further 4 s. Calculate the total distance travelled.
v_max = 18 m/s (t₁ = 6 s, t₂ = 4 s) · Distance = Area = ½vt₁ + vt₂
12. 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 15 s. Calculate the total distance travelled.
v_max = 18 m/s (t₁ = 10 s, t₂ = 15 s) · Distance = Area = ½vt₁ + vt₂

12 questions · Seed 104736 · 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 16 m/s in 9 s and then continues at a constant speed of 16 m/s for a further 9 s. Calculate the total distance travelled.
216 m
Distance is the area under the speed-time graph: triangle area = ½ × 9 × 16 = 72 m, plus rectangle area = 9 × 16 = 144 m. Total distance = 72 + 144 = 216 m.
2. 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 12 s. Calculate the total distance travelled.
272 m
Distance is the area under the speed-time graph: triangle area = ½ × 10 × 16 = 80 m, plus rectangle area = 12 × 16 = 192 m. Total distance = 80 + 192 = 272 m.
3. 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 12 s. Calculate the total distance travelled.
480 m
Distance is the area under the speed-time graph: triangle area = ½ × 8 × 30 = 120 m, plus rectangle area = 12 × 30 = 360 m. Total distance = 120 + 360 = 480 m.
4. On a speed-time graph, a train accelerates uniformly from rest to 18 m/s in 6 s and then continues at a constant speed of 18 m/s for a further 16 s. Calculate the total distance travelled.
342 m
Distance is the area under the speed-time graph: triangle area = ½ × 6 × 18 = 54 m, plus rectangle area = 16 × 18 = 288 m. Total distance = 54 + 288 = 342 m.
5. On a speed-time graph, a train accelerates uniformly from rest to 14 m/s in 5 s and then continues at a constant speed of 14 m/s for a further 15 s. Calculate the total distance travelled.
245 m
Distance is the area under the speed-time graph: triangle area = ½ × 5 × 14 = 35 m, plus rectangle area = 15 × 14 = 210 m. Total distance = 35 + 210 = 245 m.
6. On a speed-time graph, a train accelerates uniformly from rest to 10 m/s in 9 s and then continues at a constant speed of 10 m/s for a further 6 s. Calculate the total distance travelled.
105 m
Distance is the area under the speed-time graph: triangle area = ½ × 9 × 10 = 45 m, plus rectangle area = 6 × 10 = 60 m. Total distance = 45 + 60 = 105 m.
7. On a speed-time graph, a train accelerates uniformly from rest to 18 m/s in 3 s and then continues at a constant speed of 18 m/s for a further 16 s. Calculate the total distance travelled.
315 m
Distance is the area under the speed-time graph: triangle area = ½ × 3 × 18 = 27 m, plus rectangle area = 16 × 18 = 288 m. Total distance = 27 + 288 = 315 m.
8. On a speed-time graph, a train accelerates uniformly from rest to 8 m/s in 2 s and then continues at a constant speed of 8 m/s for a further 16 s. Calculate the total distance travelled.
136 m
Distance is the area under the speed-time graph: triangle area = ½ × 2 × 8 = 8 m, plus rectangle area = 16 × 8 = 128 m. Total distance = 8 + 128 = 136 m.
9. 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 17 s. Calculate the total distance travelled.
630 m
Distance is the area under the speed-time graph: triangle area = ½ × 8 × 30 = 120 m, plus rectangle area = 17 × 30 = 510 m. Total distance = 120 + 510 = 630 m.
10. On a speed-time graph, a train accelerates uniformly from rest to 34 m/s in 5 s and then continues at a constant speed of 34 m/s for a further 4 s. Calculate the total distance travelled.
221 m
Distance is the area under the speed-time graph: triangle area = ½ × 5 × 34 = 85 m, plus rectangle area = 4 × 34 = 136 m. Total distance = 85 + 136 = 221 m.
11. On a speed-time graph, a train accelerates uniformly from rest to 18 m/s in 6 s and then continues at a constant speed of 18 m/s for a further 4 s. Calculate the total distance travelled.
126 m
Distance is the area under the speed-time graph: triangle area = ½ × 6 × 18 = 54 m, plus rectangle area = 4 × 18 = 72 m. Total distance = 54 + 72 = 126 m.
12. 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 15 s. Calculate the total distance travelled.
360 m
Distance is the area under the speed-time graph: triangle area = ½ × 10 × 18 = 90 m, plus rectangle area = 15 × 18 = 270 m. Total distance = 90 + 270 = 360 m.

12 questions · Seed 104736 · Age guidance, not curriculum certification