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 42 m/s in 8 s and then continues at a constant speed of 42 m/s for a further 15 s. Calculate the total distance travelled.
v_max = 42 m/s (t₁ = 8 s, t₂ = 15 s) · Distance = Area = ½vt₁ + vt₂
2. On a speed-time graph, a train accelerates uniformly from rest to 48 m/s in 9 s and then continues at a constant speed of 48 m/s for a further 14 s. Calculate the total distance travelled.
v_max = 48 m/s (t₁ = 9 s, t₂ = 14 s) · Distance = Area = ½vt₁ + vt₂
3. On a speed-time graph, a train accelerates uniformly from rest to 26 m/s in 3 s and then continues at a constant speed of 26 m/s for a further 11 s. Calculate the total distance travelled.
v_max = 26 m/s (t₁ = 3 s, t₂ = 11 s) · Distance = Area = ½vt₁ + vt₂
4. 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 7 s. Calculate the total distance travelled.
v_max = 18 m/s (t₁ = 11 s, t₂ = 7 s) · Distance = Area = ½vt₁ + vt₂
5. On a speed-time graph, a train accelerates uniformly from rest to 34 m/s in 8 s and then continues at a constant speed of 34 m/s for a further 11 s. Calculate the total distance travelled.
v_max = 34 m/s (t₁ = 8 s, t₂ = 11 s) · Distance = Area = ½vt₁ + vt₂
6. On a speed-time graph, a train accelerates uniformly from rest to 40 m/s in 5 s and then continues at a constant speed of 40 m/s for a further 5 s. Calculate the total distance travelled.
v_max = 40 m/s (t₁ = 5 s, t₂ = 5 s) · Distance = Area = ½vt₁ + vt₂
7. On a speed-time graph, a train accelerates uniformly from rest to 44 m/s in 3 s and then continues at a constant speed of 44 m/s for a further 11 s. Calculate the total distance travelled.
v_max = 44 m/s (t₁ = 3 s, t₂ = 11 s) · Distance = Area = ½vt₁ + vt₂
8. On a speed-time graph, a train accelerates uniformly from rest to 20 m/s in 10 s and then continues at a constant speed of 20 m/s for a further 7 s. Calculate the total distance travelled.
v_max = 20 m/s (t₁ = 10 s, t₂ = 7 s) · Distance = Area = ½vt₁ + vt₂
9. 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 12 s. Calculate the total distance travelled.
v_max = 8 m/s (t₁ = 7 s, t₂ = 12 s) · Distance = Area = ½vt₁ + vt₂
10. On a speed-time graph, a train accelerates uniformly from rest to 38 m/s in 10 s and then continues at a constant speed of 38 m/s for a further 18 s. Calculate the total distance travelled.
v_max = 38 m/s (t₁ = 10 s, t₂ = 18 s) · Distance = Area = ½vt₁ + vt₂
11. On a speed-time graph, a train accelerates uniformly from rest to 38 m/s in 6 s and then continues at a constant speed of 38 m/s for a further 17 s. Calculate the total distance travelled.
v_max = 38 m/s (t₁ = 6 s, t₂ = 17 s) · Distance = Area = ½vt₁ + vt₂
12. On a speed-time graph, a train accelerates uniformly from rest to 14 m/s in 3 s and then continues at a constant speed of 14 m/s for a further 11 s. Calculate the total distance travelled.
v_max = 14 m/s (t₁ = 3 s, t₂ = 11 s) · Distance = Area = ½vt₁ + vt₂

12 questions · Seed 104731 · 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 42 m/s in 8 s and then continues at a constant speed of 42 m/s for a further 15 s. Calculate the total distance travelled.
798 m
Distance is the area under the speed-time graph: triangle area = ½ × 8 × 42 = 168 m, plus rectangle area = 15 × 42 = 630 m. Total distance = 168 + 630 = 798 m.
2. On a speed-time graph, a train accelerates uniformly from rest to 48 m/s in 9 s and then continues at a constant speed of 48 m/s for a further 14 s. Calculate the total distance travelled.
888 m
Distance is the area under the speed-time graph: triangle area = ½ × 9 × 48 = 216 m, plus rectangle area = 14 × 48 = 672 m. Total distance = 216 + 672 = 888 m.
3. On a speed-time graph, a train accelerates uniformly from rest to 26 m/s in 3 s and then continues at a constant speed of 26 m/s for a further 11 s. Calculate the total distance travelled.
325 m
Distance is the area under the speed-time graph: triangle area = ½ × 3 × 26 = 39 m, plus rectangle area = 11 × 26 = 286 m. Total distance = 39 + 286 = 325 m.
4. 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 7 s. Calculate the total distance travelled.
225 m
Distance is the area under the speed-time graph: triangle area = ½ × 11 × 18 = 99 m, plus rectangle area = 7 × 18 = 126 m. Total distance = 99 + 126 = 225 m.
5. On a speed-time graph, a train accelerates uniformly from rest to 34 m/s in 8 s and then continues at a constant speed of 34 m/s for a further 11 s. Calculate the total distance travelled.
510 m
Distance is the area under the speed-time graph: triangle area = ½ × 8 × 34 = 136 m, plus rectangle area = 11 × 34 = 374 m. Total distance = 136 + 374 = 510 m.
6. On a speed-time graph, a train accelerates uniformly from rest to 40 m/s in 5 s and then continues at a constant speed of 40 m/s for a further 5 s. Calculate the total distance travelled.
300 m
Distance is the area under the speed-time graph: triangle area = ½ × 5 × 40 = 100 m, plus rectangle area = 5 × 40 = 200 m. Total distance = 100 + 200 = 300 m.
7. On a speed-time graph, a train accelerates uniformly from rest to 44 m/s in 3 s and then continues at a constant speed of 44 m/s for a further 11 s. Calculate the total distance travelled.
550 m
Distance is the area under the speed-time graph: triangle area = ½ × 3 × 44 = 66 m, plus rectangle area = 11 × 44 = 484 m. Total distance = 66 + 484 = 550 m.
8. On a speed-time graph, a train accelerates uniformly from rest to 20 m/s in 10 s and then continues at a constant speed of 20 m/s for a further 7 s. Calculate the total distance travelled.
240 m
Distance is the area under the speed-time graph: triangle area = ½ × 10 × 20 = 100 m, plus rectangle area = 7 × 20 = 140 m. Total distance = 100 + 140 = 240 m.
9. 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 12 s. Calculate the total distance travelled.
124 m
Distance is the area under the speed-time graph: triangle area = ½ × 7 × 8 = 28 m, plus rectangle area = 12 × 8 = 96 m. Total distance = 28 + 96 = 124 m.
10. On a speed-time graph, a train accelerates uniformly from rest to 38 m/s in 10 s and then continues at a constant speed of 38 m/s for a further 18 s. Calculate the total distance travelled.
874 m
Distance is the area under the speed-time graph: triangle area = ½ × 10 × 38 = 190 m, plus rectangle area = 18 × 38 = 684 m. Total distance = 190 + 684 = 874 m.
11. On a speed-time graph, a train accelerates uniformly from rest to 38 m/s in 6 s and then continues at a constant speed of 38 m/s for a further 17 s. Calculate the total distance travelled.
760 m
Distance is the area under the speed-time graph: triangle area = ½ × 6 × 38 = 114 m, plus rectangle area = 17 × 38 = 646 m. Total distance = 114 + 646 = 760 m.
12. On a speed-time graph, a train accelerates uniformly from rest to 14 m/s in 3 s and then continues at a constant speed of 14 m/s for a further 11 s. Calculate the total distance travelled.
175 m
Distance is the area under the speed-time graph: triangle area = ½ × 3 × 14 = 21 m, plus rectangle area = 11 × 14 = 154 m. Total distance = 21 + 154 = 175 m.

12 questions · Seed 104731 · 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 42 m/s in 8 s and then continues at a constant speed of 42 m/s for a further 15 s. Calculate the total distance travelled.
v_max = 42 m/s (t₁ = 8 s, t₂ = 15 s) · Distance = Area = ½vt₁ + vt₂
2. On a speed-time graph, a train accelerates uniformly from rest to 48 m/s in 9 s and then continues at a constant speed of 48 m/s for a further 14 s. Calculate the total distance travelled.
v_max = 48 m/s (t₁ = 9 s, t₂ = 14 s) · Distance = Area = ½vt₁ + vt₂
3. On a speed-time graph, a train accelerates uniformly from rest to 26 m/s in 3 s and then continues at a constant speed of 26 m/s for a further 11 s. Calculate the total distance travelled.
v_max = 26 m/s (t₁ = 3 s, t₂ = 11 s) · Distance = Area = ½vt₁ + vt₂
4. 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 7 s. Calculate the total distance travelled.
v_max = 18 m/s (t₁ = 11 s, t₂ = 7 s) · Distance = Area = ½vt₁ + vt₂
5. On a speed-time graph, a train accelerates uniformly from rest to 34 m/s in 8 s and then continues at a constant speed of 34 m/s for a further 11 s. Calculate the total distance travelled.
v_max = 34 m/s (t₁ = 8 s, t₂ = 11 s) · Distance = Area = ½vt₁ + vt₂
6. On a speed-time graph, a train accelerates uniformly from rest to 40 m/s in 5 s and then continues at a constant speed of 40 m/s for a further 5 s. Calculate the total distance travelled.
v_max = 40 m/s (t₁ = 5 s, t₂ = 5 s) · Distance = Area = ½vt₁ + vt₂
7. On a speed-time graph, a train accelerates uniformly from rest to 44 m/s in 3 s and then continues at a constant speed of 44 m/s for a further 11 s. Calculate the total distance travelled.
v_max = 44 m/s (t₁ = 3 s, t₂ = 11 s) · Distance = Area = ½vt₁ + vt₂
8. On a speed-time graph, a train accelerates uniformly from rest to 20 m/s in 10 s and then continues at a constant speed of 20 m/s for a further 7 s. Calculate the total distance travelled.
v_max = 20 m/s (t₁ = 10 s, t₂ = 7 s) · Distance = Area = ½vt₁ + vt₂
9. 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 12 s. Calculate the total distance travelled.
v_max = 8 m/s (t₁ = 7 s, t₂ = 12 s) · Distance = Area = ½vt₁ + vt₂
10. On a speed-time graph, a train accelerates uniformly from rest to 38 m/s in 10 s and then continues at a constant speed of 38 m/s for a further 18 s. Calculate the total distance travelled.
v_max = 38 m/s (t₁ = 10 s, t₂ = 18 s) · Distance = Area = ½vt₁ + vt₂
11. On a speed-time graph, a train accelerates uniformly from rest to 38 m/s in 6 s and then continues at a constant speed of 38 m/s for a further 17 s. Calculate the total distance travelled.
v_max = 38 m/s (t₁ = 6 s, t₂ = 17 s) · Distance = Area = ½vt₁ + vt₂
12. On a speed-time graph, a train accelerates uniformly from rest to 14 m/s in 3 s and then continues at a constant speed of 14 m/s for a further 11 s. Calculate the total distance travelled.
v_max = 14 m/s (t₁ = 3 s, t₂ = 11 s) · Distance = Area = ½vt₁ + vt₂

12 questions · Seed 104731 · 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 42 m/s in 8 s and then continues at a constant speed of 42 m/s for a further 15 s. Calculate the total distance travelled.
798 m
Distance is the area under the speed-time graph: triangle area = ½ × 8 × 42 = 168 m, plus rectangle area = 15 × 42 = 630 m. Total distance = 168 + 630 = 798 m.
2. On a speed-time graph, a train accelerates uniformly from rest to 48 m/s in 9 s and then continues at a constant speed of 48 m/s for a further 14 s. Calculate the total distance travelled.
888 m
Distance is the area under the speed-time graph: triangle area = ½ × 9 × 48 = 216 m, plus rectangle area = 14 × 48 = 672 m. Total distance = 216 + 672 = 888 m.
3. On a speed-time graph, a train accelerates uniformly from rest to 26 m/s in 3 s and then continues at a constant speed of 26 m/s for a further 11 s. Calculate the total distance travelled.
325 m
Distance is the area under the speed-time graph: triangle area = ½ × 3 × 26 = 39 m, plus rectangle area = 11 × 26 = 286 m. Total distance = 39 + 286 = 325 m.
4. 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 7 s. Calculate the total distance travelled.
225 m
Distance is the area under the speed-time graph: triangle area = ½ × 11 × 18 = 99 m, plus rectangle area = 7 × 18 = 126 m. Total distance = 99 + 126 = 225 m.
5. On a speed-time graph, a train accelerates uniformly from rest to 34 m/s in 8 s and then continues at a constant speed of 34 m/s for a further 11 s. Calculate the total distance travelled.
510 m
Distance is the area under the speed-time graph: triangle area = ½ × 8 × 34 = 136 m, plus rectangle area = 11 × 34 = 374 m. Total distance = 136 + 374 = 510 m.
6. On a speed-time graph, a train accelerates uniformly from rest to 40 m/s in 5 s and then continues at a constant speed of 40 m/s for a further 5 s. Calculate the total distance travelled.
300 m
Distance is the area under the speed-time graph: triangle area = ½ × 5 × 40 = 100 m, plus rectangle area = 5 × 40 = 200 m. Total distance = 100 + 200 = 300 m.
7. On a speed-time graph, a train accelerates uniformly from rest to 44 m/s in 3 s and then continues at a constant speed of 44 m/s for a further 11 s. Calculate the total distance travelled.
550 m
Distance is the area under the speed-time graph: triangle area = ½ × 3 × 44 = 66 m, plus rectangle area = 11 × 44 = 484 m. Total distance = 66 + 484 = 550 m.
8. On a speed-time graph, a train accelerates uniformly from rest to 20 m/s in 10 s and then continues at a constant speed of 20 m/s for a further 7 s. Calculate the total distance travelled.
240 m
Distance is the area under the speed-time graph: triangle area = ½ × 10 × 20 = 100 m, plus rectangle area = 7 × 20 = 140 m. Total distance = 100 + 140 = 240 m.
9. 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 12 s. Calculate the total distance travelled.
124 m
Distance is the area under the speed-time graph: triangle area = ½ × 7 × 8 = 28 m, plus rectangle area = 12 × 8 = 96 m. Total distance = 28 + 96 = 124 m.
10. On a speed-time graph, a train accelerates uniformly from rest to 38 m/s in 10 s and then continues at a constant speed of 38 m/s for a further 18 s. Calculate the total distance travelled.
874 m
Distance is the area under the speed-time graph: triangle area = ½ × 10 × 38 = 190 m, plus rectangle area = 18 × 38 = 684 m. Total distance = 190 + 684 = 874 m.
11. On a speed-time graph, a train accelerates uniformly from rest to 38 m/s in 6 s and then continues at a constant speed of 38 m/s for a further 17 s. Calculate the total distance travelled.
760 m
Distance is the area under the speed-time graph: triangle area = ½ × 6 × 38 = 114 m, plus rectangle area = 17 × 38 = 646 m. Total distance = 114 + 646 = 760 m.
12. On a speed-time graph, a train accelerates uniformly from rest to 14 m/s in 3 s and then continues at a constant speed of 14 m/s for a further 11 s. Calculate the total distance travelled.
175 m
Distance is the area under the speed-time graph: triangle area = ½ × 3 × 14 = 21 m, plus rectangle area = 11 × 14 = 154 m. Total distance = 21 + 154 = 175 m.

12 questions · Seed 104731 · Age guidance, not curriculum certification