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 30 m/s in 9 s and then continues at a constant speed of 30 m/s for a further 16 s. Calculate the total distance travelled.
v_max = 30 m/s (t₁ = 9 s, t₂ = 16 s) · Distance = Area = ½vt₁ + vt₂
2. On a speed-time graph, a train accelerates uniformly from rest to 34 m/s in 10 s and then continues at a constant speed of 34 m/s for a further 7 s. Calculate the total distance travelled.
v_max = 34 m/s (t₁ = 10 s, t₂ = 7 s) · Distance = Area = ½vt₁ + vt₂
3. On a speed-time graph, a train accelerates uniformly from rest to 20 m/s in 2 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 = 2 s, t₂ = 15 s) · Distance = Area = ½vt₁ + vt₂
4. On a speed-time graph, a train accelerates uniformly from rest to 26 m/s in 12 s and then continues at a constant speed of 26 m/s for a further 5 s. Calculate the total distance travelled.
v_max = 26 m/s (t₁ = 12 s, t₂ = 5 s) · Distance = Area = ½vt₁ + vt₂
5. On a speed-time graph, a train accelerates uniformly from rest to 30 m/s in 12 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 = 12 s, t₂ = 5 s) · Distance = Area = ½vt₁ + vt₂
6. On a speed-time graph, a train accelerates uniformly from rest to 10 m/s in 3 s and then continues at a constant speed of 10 m/s for a further 13 s. Calculate the total distance travelled.
v_max = 10 m/s (t₁ = 3 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 2 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 = 2 s, t₂ = 12 s) · Distance = Area = ½vt₁ + vt₂
8. On a speed-time graph, a train accelerates uniformly from rest to 36 m/s in 2 s and then continues at a constant speed of 36 m/s for a further 9 s. Calculate the total distance travelled.
v_max = 36 m/s (t₁ = 2 s, t₂ = 9 s) · Distance = Area = ½vt₁ + vt₂
9. On a speed-time graph, a train accelerates uniformly from rest to 8 m/s in 12 s and then continues at a constant speed of 8 m/s for a further 18 s. Calculate the total distance travelled.
v_max = 8 m/s (t₁ = 12 s, t₂ = 18 s) · Distance = Area = ½vt₁ + vt₂
10. On a speed-time graph, a train accelerates uniformly from rest to 24 m/s in 6 s and then continues at a constant speed of 24 m/s for a further 5 s. Calculate the total distance travelled.
v_max = 24 m/s (t₁ = 6 s, t₂ = 5 s) · Distance = Area = ½vt₁ + vt₂
11. 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 12 s. Calculate the total distance travelled.
v_max = 12 m/s (t₁ = 11 s, t₂ = 12 s) · Distance = Area = ½vt₁ + vt₂
12. 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

12 questions · Seed 104738 · 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 30 m/s in 9 s and then continues at a constant speed of 30 m/s for a further 16 s. Calculate the total distance travelled.
615 m
Distance is the area under the speed-time graph: triangle area = ½ × 9 × 30 = 135 m, plus rectangle area = 16 × 30 = 480 m. Total distance = 135 + 480 = 615 m.
2. On a speed-time graph, a train accelerates uniformly from rest to 34 m/s in 10 s and then continues at a constant speed of 34 m/s for a further 7 s. Calculate the total distance travelled.
408 m
Distance is the area under the speed-time graph: triangle area = ½ × 10 × 34 = 170 m, plus rectangle area = 7 × 34 = 238 m. Total distance = 170 + 238 = 408 m.
3. On a speed-time graph, a train accelerates uniformly from rest to 20 m/s in 2 s and then continues at a constant speed of 20 m/s for a further 15 s. Calculate the total distance travelled.
320 m
Distance is the area under the speed-time graph: triangle area = ½ × 2 × 20 = 20 m, plus rectangle area = 15 × 20 = 300 m. Total distance = 20 + 300 = 320 m.
4. On a speed-time graph, a train accelerates uniformly from rest to 26 m/s in 12 s and then continues at a constant speed of 26 m/s for a further 5 s. Calculate the total distance travelled.
286 m
Distance is the area under the speed-time graph: triangle area = ½ × 12 × 26 = 156 m, plus rectangle area = 5 × 26 = 130 m. Total distance = 156 + 130 = 286 m.
5. On a speed-time graph, a train accelerates uniformly from rest to 30 m/s in 12 s and then continues at a constant speed of 30 m/s for a further 5 s. Calculate the total distance travelled.
330 m
Distance is the area under the speed-time graph: triangle area = ½ × 12 × 30 = 180 m, plus rectangle area = 5 × 30 = 150 m. Total distance = 180 + 150 = 330 m.
6. On a speed-time graph, a train accelerates uniformly from rest to 10 m/s in 3 s and then continues at a constant speed of 10 m/s for a further 13 s. Calculate the total distance travelled.
145 m
Distance is the area under the speed-time graph: triangle area = ½ × 3 × 10 = 15 m, plus rectangle area = 13 × 10 = 130 m. Total distance = 15 + 130 = 145 m.
7. On a speed-time graph, a train accelerates uniformly from rest to 16 m/s in 2 s and then continues at a constant speed of 16 m/s for a further 12 s. Calculate the total distance travelled.
208 m
Distance is the area under the speed-time graph: triangle area = ½ × 2 × 16 = 16 m, plus rectangle area = 12 × 16 = 192 m. Total distance = 16 + 192 = 208 m.
8. On a speed-time graph, a train accelerates uniformly from rest to 36 m/s in 2 s and then continues at a constant speed of 36 m/s for a further 9 s. Calculate the total distance travelled.
360 m
Distance is the area under the speed-time graph: triangle area = ½ × 2 × 36 = 36 m, plus rectangle area = 9 × 36 = 324 m. Total distance = 36 + 324 = 360 m.
9. On a speed-time graph, a train accelerates uniformly from rest to 8 m/s in 12 s and then continues at a constant speed of 8 m/s for a further 18 s. Calculate the total distance travelled.
192 m
Distance is the area under the speed-time graph: triangle area = ½ × 12 × 8 = 48 m, plus rectangle area = 18 × 8 = 144 m. Total distance = 48 + 144 = 192 m.
10. On a speed-time graph, a train accelerates uniformly from rest to 24 m/s in 6 s and then continues at a constant speed of 24 m/s for a further 5 s. Calculate the total distance travelled.
192 m
Distance is the area under the speed-time graph: triangle area = ½ × 6 × 24 = 72 m, plus rectangle area = 5 × 24 = 120 m. Total distance = 72 + 120 = 192 m.
11. 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 12 s. Calculate the total distance travelled.
210 m
Distance is the area under the speed-time graph: triangle area = ½ × 11 × 12 = 66 m, plus rectangle area = 12 × 12 = 144 m. Total distance = 66 + 144 = 210 m.
12. 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.

12 questions · Seed 104738 · 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 30 m/s in 9 s and then continues at a constant speed of 30 m/s for a further 16 s. Calculate the total distance travelled.
v_max = 30 m/s (t₁ = 9 s, t₂ = 16 s) · Distance = Area = ½vt₁ + vt₂
2. On a speed-time graph, a train accelerates uniformly from rest to 34 m/s in 10 s and then continues at a constant speed of 34 m/s for a further 7 s. Calculate the total distance travelled.
v_max = 34 m/s (t₁ = 10 s, t₂ = 7 s) · Distance = Area = ½vt₁ + vt₂
3. On a speed-time graph, a train accelerates uniformly from rest to 20 m/s in 2 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 = 2 s, t₂ = 15 s) · Distance = Area = ½vt₁ + vt₂
4. On a speed-time graph, a train accelerates uniformly from rest to 26 m/s in 12 s and then continues at a constant speed of 26 m/s for a further 5 s. Calculate the total distance travelled.
v_max = 26 m/s (t₁ = 12 s, t₂ = 5 s) · Distance = Area = ½vt₁ + vt₂
5. On a speed-time graph, a train accelerates uniformly from rest to 30 m/s in 12 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 = 12 s, t₂ = 5 s) · Distance = Area = ½vt₁ + vt₂
6. On a speed-time graph, a train accelerates uniformly from rest to 10 m/s in 3 s and then continues at a constant speed of 10 m/s for a further 13 s. Calculate the total distance travelled.
v_max = 10 m/s (t₁ = 3 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 2 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 = 2 s, t₂ = 12 s) · Distance = Area = ½vt₁ + vt₂
8. On a speed-time graph, a train accelerates uniformly from rest to 36 m/s in 2 s and then continues at a constant speed of 36 m/s for a further 9 s. Calculate the total distance travelled.
v_max = 36 m/s (t₁ = 2 s, t₂ = 9 s) · Distance = Area = ½vt₁ + vt₂
9. On a speed-time graph, a train accelerates uniformly from rest to 8 m/s in 12 s and then continues at a constant speed of 8 m/s for a further 18 s. Calculate the total distance travelled.
v_max = 8 m/s (t₁ = 12 s, t₂ = 18 s) · Distance = Area = ½vt₁ + vt₂
10. On a speed-time graph, a train accelerates uniformly from rest to 24 m/s in 6 s and then continues at a constant speed of 24 m/s for a further 5 s. Calculate the total distance travelled.
v_max = 24 m/s (t₁ = 6 s, t₂ = 5 s) · Distance = Area = ½vt₁ + vt₂
11. 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 12 s. Calculate the total distance travelled.
v_max = 12 m/s (t₁ = 11 s, t₂ = 12 s) · Distance = Area = ½vt₁ + vt₂
12. 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

12 questions · Seed 104738 · 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 30 m/s in 9 s and then continues at a constant speed of 30 m/s for a further 16 s. Calculate the total distance travelled.
615 m
Distance is the area under the speed-time graph: triangle area = ½ × 9 × 30 = 135 m, plus rectangle area = 16 × 30 = 480 m. Total distance = 135 + 480 = 615 m.
2. On a speed-time graph, a train accelerates uniformly from rest to 34 m/s in 10 s and then continues at a constant speed of 34 m/s for a further 7 s. Calculate the total distance travelled.
408 m
Distance is the area under the speed-time graph: triangle area = ½ × 10 × 34 = 170 m, plus rectangle area = 7 × 34 = 238 m. Total distance = 170 + 238 = 408 m.
3. On a speed-time graph, a train accelerates uniformly from rest to 20 m/s in 2 s and then continues at a constant speed of 20 m/s for a further 15 s. Calculate the total distance travelled.
320 m
Distance is the area under the speed-time graph: triangle area = ½ × 2 × 20 = 20 m, plus rectangle area = 15 × 20 = 300 m. Total distance = 20 + 300 = 320 m.
4. On a speed-time graph, a train accelerates uniformly from rest to 26 m/s in 12 s and then continues at a constant speed of 26 m/s for a further 5 s. Calculate the total distance travelled.
286 m
Distance is the area under the speed-time graph: triangle area = ½ × 12 × 26 = 156 m, plus rectangle area = 5 × 26 = 130 m. Total distance = 156 + 130 = 286 m.
5. On a speed-time graph, a train accelerates uniformly from rest to 30 m/s in 12 s and then continues at a constant speed of 30 m/s for a further 5 s. Calculate the total distance travelled.
330 m
Distance is the area under the speed-time graph: triangle area = ½ × 12 × 30 = 180 m, plus rectangle area = 5 × 30 = 150 m. Total distance = 180 + 150 = 330 m.
6. On a speed-time graph, a train accelerates uniformly from rest to 10 m/s in 3 s and then continues at a constant speed of 10 m/s for a further 13 s. Calculate the total distance travelled.
145 m
Distance is the area under the speed-time graph: triangle area = ½ × 3 × 10 = 15 m, plus rectangle area = 13 × 10 = 130 m. Total distance = 15 + 130 = 145 m.
7. On a speed-time graph, a train accelerates uniformly from rest to 16 m/s in 2 s and then continues at a constant speed of 16 m/s for a further 12 s. Calculate the total distance travelled.
208 m
Distance is the area under the speed-time graph: triangle area = ½ × 2 × 16 = 16 m, plus rectangle area = 12 × 16 = 192 m. Total distance = 16 + 192 = 208 m.
8. On a speed-time graph, a train accelerates uniformly from rest to 36 m/s in 2 s and then continues at a constant speed of 36 m/s for a further 9 s. Calculate the total distance travelled.
360 m
Distance is the area under the speed-time graph: triangle area = ½ × 2 × 36 = 36 m, plus rectangle area = 9 × 36 = 324 m. Total distance = 36 + 324 = 360 m.
9. On a speed-time graph, a train accelerates uniformly from rest to 8 m/s in 12 s and then continues at a constant speed of 8 m/s for a further 18 s. Calculate the total distance travelled.
192 m
Distance is the area under the speed-time graph: triangle area = ½ × 12 × 8 = 48 m, plus rectangle area = 18 × 8 = 144 m. Total distance = 48 + 144 = 192 m.
10. On a speed-time graph, a train accelerates uniformly from rest to 24 m/s in 6 s and then continues at a constant speed of 24 m/s for a further 5 s. Calculate the total distance travelled.
192 m
Distance is the area under the speed-time graph: triangle area = ½ × 6 × 24 = 72 m, plus rectangle area = 5 × 24 = 120 m. Total distance = 72 + 120 = 192 m.
11. 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 12 s. Calculate the total distance travelled.
210 m
Distance is the area under the speed-time graph: triangle area = ½ × 11 × 12 = 66 m, plus rectangle area = 12 × 12 = 144 m. Total distance = 66 + 144 = 210 m.
12. 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.

12 questions · Seed 104738 · Age guidance, not curriculum certification