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.

New variation Try interactive challenge Browse templates

Age band:Ages 13-15 Ages 16-18

Choose “Save as PDF” to keep a copy. Use your browser’s paper setting for A4 or Letter.

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 8 m/s in 2 s and then continues at a constant speed of 8 m/s for a further 5 s. Calculate the total distance travelled.
v_max = 8 m/s (t₁ = 2 s, t₂ = 5 s) · Distance = Area = ½vt₁ + vt₂
2. On a speed-time graph, a train accelerates uniformly from rest to 46 m/s in 8 s and then continues at a constant speed of 46 m/s for a further 9 s. Calculate the total distance travelled.
v_max = 46 m/s (t₁ = 8 s, t₂ = 9 s) · Distance = Area = ½vt₁ + vt₂
3. On a speed-time graph, a train accelerates uniformly from rest to 44 m/s in 10 s and then continues at a constant speed of 44 m/s for a further 4 s. Calculate the total distance travelled.
v_max = 44 m/s (t₁ = 10 s, t₂ = 4 s) · Distance = Area = ½vt₁ + vt₂
4. On a speed-time graph, a train accelerates uniformly from rest to 34 m/s in 11 s and then continues at a constant speed of 34 m/s for a further 14 s. Calculate the total distance travelled.
v_max = 34 m/s (t₁ = 11 s, t₂ = 14 s) · Distance = Area = ½vt₁ + vt₂
5. On a speed-time graph, a train accelerates uniformly from rest to 36 m/s in 11 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 = 11 s, t₂ = 9 s) · Distance = Area = ½vt₁ + vt₂
6. 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
7. On a speed-time graph, a train accelerates uniformly from rest to 44 m/s in 11 s and then continues at a constant speed of 44 m/s for a further 12 s. Calculate the total distance travelled.
v_max = 44 m/s (t₁ = 11 s, t₂ = 12 s) · Distance = Area = ½vt₁ + vt₂
8. On a speed-time graph, a train accelerates uniformly from rest to 42 m/s in 7 s and then continues at a constant speed of 42 m/s for a further 7 s. Calculate the total distance travelled.
v_max = 42 m/s (t₁ = 7 s, t₂ = 7 s) · Distance = Area = ½vt₁ + vt₂
9. On a speed-time graph, a train accelerates uniformly from rest to 42 m/s in 7 s and then continues at a constant speed of 42 m/s for a further 9 s. Calculate the total distance travelled.
v_max = 42 m/s (t₁ = 7 s, t₂ = 9 s) · Distance = Area = ½vt₁ + vt₂
10. On a speed-time graph, a train accelerates uniformly from rest to 42 m/s in 12 s and then continues at a constant speed of 42 m/s for a further 10 s. Calculate the total distance travelled.
v_max = 42 m/s (t₁ = 12 s, t₂ = 10 s) · Distance = Area = ½vt₁ + vt₂
11. On a speed-time graph, a train accelerates uniformly from rest to 50 m/s in 10 s and then continues at a constant speed of 50 m/s for a further 13 s. Calculate the total distance travelled.
v_max = 50 m/s (t₁ = 10 s, t₂ = 13 s) · Distance = Area = ½vt₁ + vt₂
12. On a speed-time graph, a train accelerates uniformly from rest to 32 m/s in 6 s and then continues at a constant speed of 32 m/s for a further 14 s. Calculate the total distance travelled.
v_max = 32 m/s (t₁ = 6 s, t₂ = 14 s) · Distance = Area = ½vt₁ + vt₂

12 questions · Seed 104734 · 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 8 m/s in 2 s and then continues at a constant speed of 8 m/s for a further 5 s. Calculate the total distance travelled.
48 m
Distance is the area under the speed-time graph: triangle area = ½ × 2 × 8 = 8 m, plus rectangle area = 5 × 8 = 40 m. Total distance = 8 + 40 = 48 m.
2. On a speed-time graph, a train accelerates uniformly from rest to 46 m/s in 8 s and then continues at a constant speed of 46 m/s for a further 9 s. Calculate the total distance travelled.
598 m
Distance is the area under the speed-time graph: triangle area = ½ × 8 × 46 = 184 m, plus rectangle area = 9 × 46 = 414 m. Total distance = 184 + 414 = 598 m.
3. On a speed-time graph, a train accelerates uniformly from rest to 44 m/s in 10 s and then continues at a constant speed of 44 m/s for a further 4 s. Calculate the total distance travelled.
396 m
Distance is the area under the speed-time graph: triangle area = ½ × 10 × 44 = 220 m, plus rectangle area = 4 × 44 = 176 m. Total distance = 220 + 176 = 396 m.
4. On a speed-time graph, a train accelerates uniformly from rest to 34 m/s in 11 s and then continues at a constant speed of 34 m/s for a further 14 s. Calculate the total distance travelled.
663 m
Distance is the area under the speed-time graph: triangle area = ½ × 11 × 34 = 187 m, plus rectangle area = 14 × 34 = 476 m. Total distance = 187 + 476 = 663 m.
5. On a speed-time graph, a train accelerates uniformly from rest to 36 m/s in 11 s and then continues at a constant speed of 36 m/s for a further 9 s. Calculate the total distance travelled.
522 m
Distance is the area under the speed-time graph: triangle area = ½ × 11 × 36 = 198 m, plus rectangle area = 9 × 36 = 324 m. Total distance = 198 + 324 = 522 m.
6. 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.
7. On a speed-time graph, a train accelerates uniformly from rest to 44 m/s in 11 s and then continues at a constant speed of 44 m/s for a further 12 s. Calculate the total distance travelled.
770 m
Distance is the area under the speed-time graph: triangle area = ½ × 11 × 44 = 242 m, plus rectangle area = 12 × 44 = 528 m. Total distance = 242 + 528 = 770 m.
8. On a speed-time graph, a train accelerates uniformly from rest to 42 m/s in 7 s and then continues at a constant speed of 42 m/s for a further 7 s. Calculate the total distance travelled.
441 m
Distance is the area under the speed-time graph: triangle area = ½ × 7 × 42 = 147 m, plus rectangle area = 7 × 42 = 294 m. Total distance = 147 + 294 = 441 m.
9. On a speed-time graph, a train accelerates uniformly from rest to 42 m/s in 7 s and then continues at a constant speed of 42 m/s for a further 9 s. Calculate the total distance travelled.
525 m
Distance is the area under the speed-time graph: triangle area = ½ × 7 × 42 = 147 m, plus rectangle area = 9 × 42 = 378 m. Total distance = 147 + 378 = 525 m.
10. On a speed-time graph, a train accelerates uniformly from rest to 42 m/s in 12 s and then continues at a constant speed of 42 m/s for a further 10 s. Calculate the total distance travelled.
672 m
Distance is the area under the speed-time graph: triangle area = ½ × 12 × 42 = 252 m, plus rectangle area = 10 × 42 = 420 m. Total distance = 252 + 420 = 672 m.
11. On a speed-time graph, a train accelerates uniformly from rest to 50 m/s in 10 s and then continues at a constant speed of 50 m/s for a further 13 s. Calculate the total distance travelled.
900 m
Distance is the area under the speed-time graph: triangle area = ½ × 10 × 50 = 250 m, plus rectangle area = 13 × 50 = 650 m. Total distance = 250 + 650 = 900 m.
12. On a speed-time graph, a train accelerates uniformly from rest to 32 m/s in 6 s and then continues at a constant speed of 32 m/s for a further 14 s. Calculate the total distance travelled.
544 m
Distance is the area under the speed-time graph: triangle area = ½ × 6 × 32 = 96 m, plus rectangle area = 14 × 32 = 448 m. Total distance = 96 + 448 = 544 m.

12 questions · Seed 104734 · 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 8 m/s in 2 s and then continues at a constant speed of 8 m/s for a further 5 s. Calculate the total distance travelled.
v_max = 8 m/s (t₁ = 2 s, t₂ = 5 s) · Distance = Area = ½vt₁ + vt₂
2. On a speed-time graph, a train accelerates uniformly from rest to 46 m/s in 8 s and then continues at a constant speed of 46 m/s for a further 9 s. Calculate the total distance travelled.
v_max = 46 m/s (t₁ = 8 s, t₂ = 9 s) · Distance = Area = ½vt₁ + vt₂
3. On a speed-time graph, a train accelerates uniformly from rest to 44 m/s in 10 s and then continues at a constant speed of 44 m/s for a further 4 s. Calculate the total distance travelled.
v_max = 44 m/s (t₁ = 10 s, t₂ = 4 s) · Distance = Area = ½vt₁ + vt₂
4. On a speed-time graph, a train accelerates uniformly from rest to 34 m/s in 11 s and then continues at a constant speed of 34 m/s for a further 14 s. Calculate the total distance travelled.
v_max = 34 m/s (t₁ = 11 s, t₂ = 14 s) · Distance = Area = ½vt₁ + vt₂
5. On a speed-time graph, a train accelerates uniformly from rest to 36 m/s in 11 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 = 11 s, t₂ = 9 s) · Distance = Area = ½vt₁ + vt₂
6. 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
7. On a speed-time graph, a train accelerates uniformly from rest to 44 m/s in 11 s and then continues at a constant speed of 44 m/s for a further 12 s. Calculate the total distance travelled.
v_max = 44 m/s (t₁ = 11 s, t₂ = 12 s) · Distance = Area = ½vt₁ + vt₂
8. On a speed-time graph, a train accelerates uniformly from rest to 42 m/s in 7 s and then continues at a constant speed of 42 m/s for a further 7 s. Calculate the total distance travelled.
v_max = 42 m/s (t₁ = 7 s, t₂ = 7 s) · Distance = Area = ½vt₁ + vt₂
9. On a speed-time graph, a train accelerates uniformly from rest to 42 m/s in 7 s and then continues at a constant speed of 42 m/s for a further 9 s. Calculate the total distance travelled.
v_max = 42 m/s (t₁ = 7 s, t₂ = 9 s) · Distance = Area = ½vt₁ + vt₂
10. On a speed-time graph, a train accelerates uniformly from rest to 42 m/s in 12 s and then continues at a constant speed of 42 m/s for a further 10 s. Calculate the total distance travelled.
v_max = 42 m/s (t₁ = 12 s, t₂ = 10 s) · Distance = Area = ½vt₁ + vt₂
11. On a speed-time graph, a train accelerates uniformly from rest to 50 m/s in 10 s and then continues at a constant speed of 50 m/s for a further 13 s. Calculate the total distance travelled.
v_max = 50 m/s (t₁ = 10 s, t₂ = 13 s) · Distance = Area = ½vt₁ + vt₂
12. On a speed-time graph, a train accelerates uniformly from rest to 32 m/s in 6 s and then continues at a constant speed of 32 m/s for a further 14 s. Calculate the total distance travelled.
v_max = 32 m/s (t₁ = 6 s, t₂ = 14 s) · Distance = Area = ½vt₁ + vt₂

12 questions · Seed 104734 · 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 8 m/s in 2 s and then continues at a constant speed of 8 m/s for a further 5 s. Calculate the total distance travelled.
48 m
Distance is the area under the speed-time graph: triangle area = ½ × 2 × 8 = 8 m, plus rectangle area = 5 × 8 = 40 m. Total distance = 8 + 40 = 48 m.
2. On a speed-time graph, a train accelerates uniformly from rest to 46 m/s in 8 s and then continues at a constant speed of 46 m/s for a further 9 s. Calculate the total distance travelled.
598 m
Distance is the area under the speed-time graph: triangle area = ½ × 8 × 46 = 184 m, plus rectangle area = 9 × 46 = 414 m. Total distance = 184 + 414 = 598 m.
3. On a speed-time graph, a train accelerates uniformly from rest to 44 m/s in 10 s and then continues at a constant speed of 44 m/s for a further 4 s. Calculate the total distance travelled.
396 m
Distance is the area under the speed-time graph: triangle area = ½ × 10 × 44 = 220 m, plus rectangle area = 4 × 44 = 176 m. Total distance = 220 + 176 = 396 m.
4. On a speed-time graph, a train accelerates uniformly from rest to 34 m/s in 11 s and then continues at a constant speed of 34 m/s for a further 14 s. Calculate the total distance travelled.
663 m
Distance is the area under the speed-time graph: triangle area = ½ × 11 × 34 = 187 m, plus rectangle area = 14 × 34 = 476 m. Total distance = 187 + 476 = 663 m.
5. On a speed-time graph, a train accelerates uniformly from rest to 36 m/s in 11 s and then continues at a constant speed of 36 m/s for a further 9 s. Calculate the total distance travelled.
522 m
Distance is the area under the speed-time graph: triangle area = ½ × 11 × 36 = 198 m, plus rectangle area = 9 × 36 = 324 m. Total distance = 198 + 324 = 522 m.
6. 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.
7. On a speed-time graph, a train accelerates uniformly from rest to 44 m/s in 11 s and then continues at a constant speed of 44 m/s for a further 12 s. Calculate the total distance travelled.
770 m
Distance is the area under the speed-time graph: triangle area = ½ × 11 × 44 = 242 m, plus rectangle area = 12 × 44 = 528 m. Total distance = 242 + 528 = 770 m.
8. On a speed-time graph, a train accelerates uniformly from rest to 42 m/s in 7 s and then continues at a constant speed of 42 m/s for a further 7 s. Calculate the total distance travelled.
441 m
Distance is the area under the speed-time graph: triangle area = ½ × 7 × 42 = 147 m, plus rectangle area = 7 × 42 = 294 m. Total distance = 147 + 294 = 441 m.
9. On a speed-time graph, a train accelerates uniformly from rest to 42 m/s in 7 s and then continues at a constant speed of 42 m/s for a further 9 s. Calculate the total distance travelled.
525 m
Distance is the area under the speed-time graph: triangle area = ½ × 7 × 42 = 147 m, plus rectangle area = 9 × 42 = 378 m. Total distance = 147 + 378 = 525 m.
10. On a speed-time graph, a train accelerates uniformly from rest to 42 m/s in 12 s and then continues at a constant speed of 42 m/s for a further 10 s. Calculate the total distance travelled.
672 m
Distance is the area under the speed-time graph: triangle area = ½ × 12 × 42 = 252 m, plus rectangle area = 10 × 42 = 420 m. Total distance = 252 + 420 = 672 m.
11. On a speed-time graph, a train accelerates uniformly from rest to 50 m/s in 10 s and then continues at a constant speed of 50 m/s for a further 13 s. Calculate the total distance travelled.
900 m
Distance is the area under the speed-time graph: triangle area = ½ × 10 × 50 = 250 m, plus rectangle area = 13 × 50 = 650 m. Total distance = 250 + 650 = 900 m.
12. On a speed-time graph, a train accelerates uniformly from rest to 32 m/s in 6 s and then continues at a constant speed of 32 m/s for a further 14 s. Calculate the total distance travelled.
544 m
Distance is the area under the speed-time graph: triangle area = ½ × 6 × 32 = 96 m, plus rectangle area = 14 × 32 = 448 m. Total distance = 96 + 448 = 544 m.

12 questions · Seed 104734 · Age guidance, not curriculum certification