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 18 m/s in 12 s and then continues at a constant speed of 18 m/s for a further 8 s. Calculate the total distance travelled.
v_max = 18 m/s (t₁ = 12 s, t₂ = 8 s) · Distance = Area = ½vt₁ + vt₂
2. On a speed-time graph, a train accelerates uniformly from rest to 24 m/s in 3 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 = 3 s, t₂ = 17 s) · Distance = Area = ½vt₁ + vt₂
3. On a speed-time graph, a train accelerates uniformly from rest to 50 m/s in 3 s and then continues at a constant speed of 50 m/s for a further 16 s. Calculate the total distance travelled.
v_max = 50 m/s (t₁ = 3 s, t₂ = 16 s) · Distance = Area = ½vt₁ + vt₂
4. 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
5. On a speed-time graph, a train accelerates uniformly from rest to 26 m/s in 2 s and then continues at a constant speed of 26 m/s for a further 8 s. Calculate the total distance travelled.
v_max = 26 m/s (t₁ = 2 s, t₂ = 8 s) · Distance = Area = ½vt₁ + vt₂
6. On a speed-time graph, a train accelerates uniformly from rest to 38 m/s in 3 s and then continues at a constant speed of 38 m/s for a further 11 s. Calculate the total distance travelled.
v_max = 38 m/s (t₁ = 3 s, t₂ = 11 s) · Distance = Area = ½vt₁ + vt₂
7. On a speed-time graph, a train accelerates uniformly from rest to 40 m/s in 3 s and then continues at a constant speed of 40 m/s for a further 17 s. Calculate the total distance travelled.
v_max = 40 m/s (t₁ = 3 s, t₂ = 17 s) · Distance = Area = ½vt₁ + vt₂
8. On a speed-time graph, a train accelerates uniformly from rest to 36 m/s in 6 s and then continues at a constant speed of 36 m/s for a further 12 s. Calculate the total distance travelled.
v_max = 36 m/s (t₁ = 6 s, t₂ = 12 s) · Distance = Area = ½vt₁ + vt₂
9. On a speed-time graph, a train accelerates uniformly from rest to 16 m/s in 6 s and then continues at a constant speed of 16 m/s for a further 18 s. Calculate the total distance travelled.
v_max = 16 m/s (t₁ = 6 s, t₂ = 18 s) · Distance = Area = ½vt₁ + vt₂
10. 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 18 s. Calculate the total distance travelled.
v_max = 8 m/s (t₁ = 9 s, t₂ = 18 s) · Distance = Area = ½vt₁ + vt₂
11. On a speed-time graph, a train accelerates uniformly from rest to 50 m/s in 3 s and then continues at a constant speed of 50 m/s for a further 6 s. Calculate the total distance travelled.
v_max = 50 m/s (t₁ = 3 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 7 s and then continues at a constant speed of 8 m/s for a further 9 s. Calculate the total distance travelled.
v_max = 8 m/s (t₁ = 7 s, t₂ = 9 s) · Distance = Area = ½vt₁ + vt₂

12 questions · Seed 51 · 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 18 m/s in 12 s and then continues at a constant speed of 18 m/s for a further 8 s. Calculate the total distance travelled.
252 m
Distance is the area under the speed-time graph: triangle area = ½ × 12 × 18 = 108 m, plus rectangle area = 8 × 18 = 144 m. Total distance = 108 + 144 = 252 m.
2. On a speed-time graph, a train accelerates uniformly from rest to 24 m/s in 3 s and then continues at a constant speed of 24 m/s for a further 17 s. Calculate the total distance travelled.
444 m
Distance is the area under the speed-time graph: triangle area = ½ × 3 × 24 = 36 m, plus rectangle area = 17 × 24 = 408 m. Total distance = 36 + 408 = 444 m.
3. On a speed-time graph, a train accelerates uniformly from rest to 50 m/s in 3 s and then continues at a constant speed of 50 m/s for a further 16 s. Calculate the total distance travelled.
875 m
Distance is the area under the speed-time graph: triangle area = ½ × 3 × 50 = 75 m, plus rectangle area = 16 × 50 = 800 m. Total distance = 75 + 800 = 875 m.
4. 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.
5. On a speed-time graph, a train accelerates uniformly from rest to 26 m/s in 2 s and then continues at a constant speed of 26 m/s for a further 8 s. Calculate the total distance travelled.
234 m
Distance is the area under the speed-time graph: triangle area = ½ × 2 × 26 = 26 m, plus rectangle area = 8 × 26 = 208 m. Total distance = 26 + 208 = 234 m.
6. On a speed-time graph, a train accelerates uniformly from rest to 38 m/s in 3 s and then continues at a constant speed of 38 m/s for a further 11 s. Calculate the total distance travelled.
475 m
Distance is the area under the speed-time graph: triangle area = ½ × 3 × 38 = 57 m, plus rectangle area = 11 × 38 = 418 m. Total distance = 57 + 418 = 475 m.
7. On a speed-time graph, a train accelerates uniformly from rest to 40 m/s in 3 s and then continues at a constant speed of 40 m/s for a further 17 s. Calculate the total distance travelled.
740 m
Distance is the area under the speed-time graph: triangle area = ½ × 3 × 40 = 60 m, plus rectangle area = 17 × 40 = 680 m. Total distance = 60 + 680 = 740 m.
8. On a speed-time graph, a train accelerates uniformly from rest to 36 m/s in 6 s and then continues at a constant speed of 36 m/s for a further 12 s. Calculate the total distance travelled.
540 m
Distance is the area under the speed-time graph: triangle area = ½ × 6 × 36 = 108 m, plus rectangle area = 12 × 36 = 432 m. Total distance = 108 + 432 = 540 m.
9. On a speed-time graph, a train accelerates uniformly from rest to 16 m/s in 6 s and then continues at a constant speed of 16 m/s for a further 18 s. Calculate the total distance travelled.
336 m
Distance is the area under the speed-time graph: triangle area = ½ × 6 × 16 = 48 m, plus rectangle area = 18 × 16 = 288 m. Total distance = 48 + 288 = 336 m.
10. 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 18 s. Calculate the total distance travelled.
180 m
Distance is the area under the speed-time graph: triangle area = ½ × 9 × 8 = 36 m, plus rectangle area = 18 × 8 = 144 m. Total distance = 36 + 144 = 180 m.
11. On a speed-time graph, a train accelerates uniformly from rest to 50 m/s in 3 s and then continues at a constant speed of 50 m/s for a further 6 s. Calculate the total distance travelled.
375 m
Distance is the area under the speed-time graph: triangle area = ½ × 3 × 50 = 75 m, plus rectangle area = 6 × 50 = 300 m. Total distance = 75 + 300 = 375 m.
12. On a speed-time graph, a train accelerates uniformly from rest to 8 m/s in 7 s and then continues at a constant speed of 8 m/s for a further 9 s. Calculate the total distance travelled.
100 m
Distance is the area under the speed-time graph: triangle area = ½ × 7 × 8 = 28 m, plus rectangle area = 9 × 8 = 72 m. Total distance = 28 + 72 = 100 m.

12 questions · Seed 51 · 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 18 m/s in 12 s and then continues at a constant speed of 18 m/s for a further 8 s. Calculate the total distance travelled.
v_max = 18 m/s (t₁ = 12 s, t₂ = 8 s) · Distance = Area = ½vt₁ + vt₂
2. On a speed-time graph, a train accelerates uniformly from rest to 24 m/s in 3 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 = 3 s, t₂ = 17 s) · Distance = Area = ½vt₁ + vt₂
3. On a speed-time graph, a train accelerates uniformly from rest to 50 m/s in 3 s and then continues at a constant speed of 50 m/s for a further 16 s. Calculate the total distance travelled.
v_max = 50 m/s (t₁ = 3 s, t₂ = 16 s) · Distance = Area = ½vt₁ + vt₂
4. 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
5. On a speed-time graph, a train accelerates uniformly from rest to 26 m/s in 2 s and then continues at a constant speed of 26 m/s for a further 8 s. Calculate the total distance travelled.
v_max = 26 m/s (t₁ = 2 s, t₂ = 8 s) · Distance = Area = ½vt₁ + vt₂
6. On a speed-time graph, a train accelerates uniformly from rest to 38 m/s in 3 s and then continues at a constant speed of 38 m/s for a further 11 s. Calculate the total distance travelled.
v_max = 38 m/s (t₁ = 3 s, t₂ = 11 s) · Distance = Area = ½vt₁ + vt₂
7. On a speed-time graph, a train accelerates uniformly from rest to 40 m/s in 3 s and then continues at a constant speed of 40 m/s for a further 17 s. Calculate the total distance travelled.
v_max = 40 m/s (t₁ = 3 s, t₂ = 17 s) · Distance = Area = ½vt₁ + vt₂
8. On a speed-time graph, a train accelerates uniformly from rest to 36 m/s in 6 s and then continues at a constant speed of 36 m/s for a further 12 s. Calculate the total distance travelled.
v_max = 36 m/s (t₁ = 6 s, t₂ = 12 s) · Distance = Area = ½vt₁ + vt₂
9. On a speed-time graph, a train accelerates uniformly from rest to 16 m/s in 6 s and then continues at a constant speed of 16 m/s for a further 18 s. Calculate the total distance travelled.
v_max = 16 m/s (t₁ = 6 s, t₂ = 18 s) · Distance = Area = ½vt₁ + vt₂
10. 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 18 s. Calculate the total distance travelled.
v_max = 8 m/s (t₁ = 9 s, t₂ = 18 s) · Distance = Area = ½vt₁ + vt₂
11. On a speed-time graph, a train accelerates uniformly from rest to 50 m/s in 3 s and then continues at a constant speed of 50 m/s for a further 6 s. Calculate the total distance travelled.
v_max = 50 m/s (t₁ = 3 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 7 s and then continues at a constant speed of 8 m/s for a further 9 s. Calculate the total distance travelled.
v_max = 8 m/s (t₁ = 7 s, t₂ = 9 s) · Distance = Area = ½vt₁ + vt₂

12 questions · Seed 51 · 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 18 m/s in 12 s and then continues at a constant speed of 18 m/s for a further 8 s. Calculate the total distance travelled.
252 m
Distance is the area under the speed-time graph: triangle area = ½ × 12 × 18 = 108 m, plus rectangle area = 8 × 18 = 144 m. Total distance = 108 + 144 = 252 m.
2. On a speed-time graph, a train accelerates uniformly from rest to 24 m/s in 3 s and then continues at a constant speed of 24 m/s for a further 17 s. Calculate the total distance travelled.
444 m
Distance is the area under the speed-time graph: triangle area = ½ × 3 × 24 = 36 m, plus rectangle area = 17 × 24 = 408 m. Total distance = 36 + 408 = 444 m.
3. On a speed-time graph, a train accelerates uniformly from rest to 50 m/s in 3 s and then continues at a constant speed of 50 m/s for a further 16 s. Calculate the total distance travelled.
875 m
Distance is the area under the speed-time graph: triangle area = ½ × 3 × 50 = 75 m, plus rectangle area = 16 × 50 = 800 m. Total distance = 75 + 800 = 875 m.
4. 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.
5. On a speed-time graph, a train accelerates uniformly from rest to 26 m/s in 2 s and then continues at a constant speed of 26 m/s for a further 8 s. Calculate the total distance travelled.
234 m
Distance is the area under the speed-time graph: triangle area = ½ × 2 × 26 = 26 m, plus rectangle area = 8 × 26 = 208 m. Total distance = 26 + 208 = 234 m.
6. On a speed-time graph, a train accelerates uniformly from rest to 38 m/s in 3 s and then continues at a constant speed of 38 m/s for a further 11 s. Calculate the total distance travelled.
475 m
Distance is the area under the speed-time graph: triangle area = ½ × 3 × 38 = 57 m, plus rectangle area = 11 × 38 = 418 m. Total distance = 57 + 418 = 475 m.
7. On a speed-time graph, a train accelerates uniformly from rest to 40 m/s in 3 s and then continues at a constant speed of 40 m/s for a further 17 s. Calculate the total distance travelled.
740 m
Distance is the area under the speed-time graph: triangle area = ½ × 3 × 40 = 60 m, plus rectangle area = 17 × 40 = 680 m. Total distance = 60 + 680 = 740 m.
8. On a speed-time graph, a train accelerates uniformly from rest to 36 m/s in 6 s and then continues at a constant speed of 36 m/s for a further 12 s. Calculate the total distance travelled.
540 m
Distance is the area under the speed-time graph: triangle area = ½ × 6 × 36 = 108 m, plus rectangle area = 12 × 36 = 432 m. Total distance = 108 + 432 = 540 m.
9. On a speed-time graph, a train accelerates uniformly from rest to 16 m/s in 6 s and then continues at a constant speed of 16 m/s for a further 18 s. Calculate the total distance travelled.
336 m
Distance is the area under the speed-time graph: triangle area = ½ × 6 × 16 = 48 m, plus rectangle area = 18 × 16 = 288 m. Total distance = 48 + 288 = 336 m.
10. 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 18 s. Calculate the total distance travelled.
180 m
Distance is the area under the speed-time graph: triangle area = ½ × 9 × 8 = 36 m, plus rectangle area = 18 × 8 = 144 m. Total distance = 36 + 144 = 180 m.
11. On a speed-time graph, a train accelerates uniformly from rest to 50 m/s in 3 s and then continues at a constant speed of 50 m/s for a further 6 s. Calculate the total distance travelled.
375 m
Distance is the area under the speed-time graph: triangle area = ½ × 3 × 50 = 75 m, plus rectangle area = 6 × 50 = 300 m. Total distance = 75 + 300 = 375 m.
12. On a speed-time graph, a train accelerates uniformly from rest to 8 m/s in 7 s and then continues at a constant speed of 8 m/s for a further 9 s. Calculate the total distance travelled.
100 m
Distance is the area under the speed-time graph: triangle area = ½ × 7 × 8 = 28 m, plus rectangle area = 9 × 8 = 72 m. Total distance = 28 + 72 = 100 m.

12 questions · Seed 51 · Age guidance, not curriculum certification