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 18 m/s in 7 s and then continues at a constant speed of 18 m/s for a further 10 s. Calculate the total distance travelled.
v_max = 18 m/s (t₁ = 7 s, t₂ = 10 s) · Distance = Area = ½vt₁ + vt₂
2. 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 4 s. Calculate the total distance travelled.
v_max = 8 m/s (t₁ = 9 s, t₂ = 4 s) · Distance = Area = ½vt₁ + vt₂
3. On a speed-time graph, a train accelerates uniformly from rest to 28 m/s in 3 s and then continues at a constant speed of 28 m/s for a further 13 s. Calculate the total distance travelled.
v_max = 28 m/s (t₁ = 3 s, t₂ = 13 s) · Distance = Area = ½vt₁ + vt₂
4. On a speed-time graph, a train accelerates uniformly from rest to 42 m/s in 3 s and then continues at a constant speed of 42 m/s for a further 8 s. Calculate the total distance travelled.
v_max = 42 m/s (t₁ = 3 s, t₂ = 8 s) · Distance = Area = ½vt₁ + vt₂
5. On a speed-time graph, a train accelerates uniformly from rest to 10 m/s in 7 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 = 7 s, t₂ = 13 s) · Distance = Area = ½vt₁ + vt₂
6. On a speed-time graph, a train accelerates uniformly from rest to 38 m/s in 9 s and then continues at a constant speed of 38 m/s for a further 15 s. Calculate the total distance travelled.
v_max = 38 m/s (t₁ = 9 s, t₂ = 15 s) · Distance = Area = ½vt₁ + vt₂
7. On a speed-time graph, a train accelerates uniformly from rest to 18 m/s in 8 s and then continues at a constant speed of 18 m/s for a further 12 s. Calculate the total distance travelled.
v_max = 18 m/s (t₁ = 8 s, t₂ = 12 s) · Distance = Area = ½vt₁ + vt₂
8. On a speed-time graph, a train accelerates uniformly from rest to 26 m/s in 11 s and then continues at a constant speed of 26 m/s for a further 19 s. Calculate the total distance travelled.
v_max = 26 m/s (t₁ = 11 s, t₂ = 19 s) · Distance = Area = ½vt₁ + vt₂
9. On a speed-time graph, a train accelerates uniformly from rest to 26 m/s in 7 s and then continues at a constant speed of 26 m/s for a further 15 s. Calculate the total distance travelled.
v_max = 26 m/s (t₁ = 7 s, t₂ = 15 s) · Distance = Area = ½vt₁ + vt₂
10. On a speed-time graph, a train accelerates uniformly from rest to 40 m/s in 10 s and then continues at a constant speed of 40 m/s for a further 10 s. Calculate the total distance travelled.
v_max = 40 m/s (t₁ = 10 s, t₂ = 10 s) · Distance = Area = ½vt₁ + vt₂
11. On a speed-time graph, a train accelerates uniformly from rest to 14 m/s in 10 s and then continues at a constant speed of 14 m/s for a further 17 s. Calculate the total distance travelled.
v_max = 14 m/s (t₁ = 10 s, t₂ = 17 s) · Distance = Area = ½vt₁ + vt₂
12. On a speed-time graph, a train accelerates uniformly from rest to 28 m/s in 4 s and then continues at a constant speed of 28 m/s for a further 7 s. Calculate the total distance travelled.
v_max = 28 m/s (t₁ = 4 s, t₂ = 7 s) · Distance = Area = ½vt₁ + vt₂

12 questions · Seed 52 · 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 18 m/s in 7 s and then continues at a constant speed of 18 m/s for a further 10 s. Calculate the total distance travelled.
243 m
Distance is the area under the speed-time graph: triangle area = ½ × 7 × 18 = 63 m, plus rectangle area = 10 × 18 = 180 m. Total distance = 63 + 180 = 243 m.
2. 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 4 s. Calculate the total distance travelled.
68 m
Distance is the area under the speed-time graph: triangle area = ½ × 9 × 8 = 36 m, plus rectangle area = 4 × 8 = 32 m. Total distance = 36 + 32 = 68 m.
3. On a speed-time graph, a train accelerates uniformly from rest to 28 m/s in 3 s and then continues at a constant speed of 28 m/s for a further 13 s. Calculate the total distance travelled.
406 m
Distance is the area under the speed-time graph: triangle area = ½ × 3 × 28 = 42 m, plus rectangle area = 13 × 28 = 364 m. Total distance = 42 + 364 = 406 m.
4. On a speed-time graph, a train accelerates uniformly from rest to 42 m/s in 3 s and then continues at a constant speed of 42 m/s for a further 8 s. Calculate the total distance travelled.
399 m
Distance is the area under the speed-time graph: triangle area = ½ × 3 × 42 = 63 m, plus rectangle area = 8 × 42 = 336 m. Total distance = 63 + 336 = 399 m.
5. On a speed-time graph, a train accelerates uniformly from rest to 10 m/s in 7 s and then continues at a constant speed of 10 m/s for a further 13 s. Calculate the total distance travelled.
165 m
Distance is the area under the speed-time graph: triangle area = ½ × 7 × 10 = 35 m, plus rectangle area = 13 × 10 = 130 m. Total distance = 35 + 130 = 165 m.
6. On a speed-time graph, a train accelerates uniformly from rest to 38 m/s in 9 s and then continues at a constant speed of 38 m/s for a further 15 s. Calculate the total distance travelled.
741 m
Distance is the area under the speed-time graph: triangle area = ½ × 9 × 38 = 171 m, plus rectangle area = 15 × 38 = 570 m. Total distance = 171 + 570 = 741 m.
7. On a speed-time graph, a train accelerates uniformly from rest to 18 m/s in 8 s and then continues at a constant speed of 18 m/s for a further 12 s. Calculate the total distance travelled.
288 m
Distance is the area under the speed-time graph: triangle area = ½ × 8 × 18 = 72 m, plus rectangle area = 12 × 18 = 216 m. Total distance = 72 + 216 = 288 m.
8. On a speed-time graph, a train accelerates uniformly from rest to 26 m/s in 11 s and then continues at a constant speed of 26 m/s for a further 19 s. Calculate the total distance travelled.
637 m
Distance is the area under the speed-time graph: triangle area = ½ × 11 × 26 = 143 m, plus rectangle area = 19 × 26 = 494 m. Total distance = 143 + 494 = 637 m.
9. On a speed-time graph, a train accelerates uniformly from rest to 26 m/s in 7 s and then continues at a constant speed of 26 m/s for a further 15 s. Calculate the total distance travelled.
481 m
Distance is the area under the speed-time graph: triangle area = ½ × 7 × 26 = 91 m, plus rectangle area = 15 × 26 = 390 m. Total distance = 91 + 390 = 481 m.
10. On a speed-time graph, a train accelerates uniformly from rest to 40 m/s in 10 s and then continues at a constant speed of 40 m/s for a further 10 s. Calculate the total distance travelled.
600 m
Distance is the area under the speed-time graph: triangle area = ½ × 10 × 40 = 200 m, plus rectangle area = 10 × 40 = 400 m. Total distance = 200 + 400 = 600 m.
11. On a speed-time graph, a train accelerates uniformly from rest to 14 m/s in 10 s and then continues at a constant speed of 14 m/s for a further 17 s. Calculate the total distance travelled.
308 m
Distance is the area under the speed-time graph: triangle area = ½ × 10 × 14 = 70 m, plus rectangle area = 17 × 14 = 238 m. Total distance = 70 + 238 = 308 m.
12. On a speed-time graph, a train accelerates uniformly from rest to 28 m/s in 4 s and then continues at a constant speed of 28 m/s for a further 7 s. Calculate the total distance travelled.
252 m
Distance is the area under the speed-time graph: triangle area = ½ × 4 × 28 = 56 m, plus rectangle area = 7 × 28 = 196 m. Total distance = 56 + 196 = 252 m.

12 questions · Seed 52 · 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 18 m/s in 7 s and then continues at a constant speed of 18 m/s for a further 10 s. Calculate the total distance travelled.
v_max = 18 m/s (t₁ = 7 s, t₂ = 10 s) · Distance = Area = ½vt₁ + vt₂
2. 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 4 s. Calculate the total distance travelled.
v_max = 8 m/s (t₁ = 9 s, t₂ = 4 s) · Distance = Area = ½vt₁ + vt₂
3. On a speed-time graph, a train accelerates uniformly from rest to 28 m/s in 3 s and then continues at a constant speed of 28 m/s for a further 13 s. Calculate the total distance travelled.
v_max = 28 m/s (t₁ = 3 s, t₂ = 13 s) · Distance = Area = ½vt₁ + vt₂
4. On a speed-time graph, a train accelerates uniformly from rest to 42 m/s in 3 s and then continues at a constant speed of 42 m/s for a further 8 s. Calculate the total distance travelled.
v_max = 42 m/s (t₁ = 3 s, t₂ = 8 s) · Distance = Area = ½vt₁ + vt₂
5. On a speed-time graph, a train accelerates uniformly from rest to 10 m/s in 7 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 = 7 s, t₂ = 13 s) · Distance = Area = ½vt₁ + vt₂
6. On a speed-time graph, a train accelerates uniformly from rest to 38 m/s in 9 s and then continues at a constant speed of 38 m/s for a further 15 s. Calculate the total distance travelled.
v_max = 38 m/s (t₁ = 9 s, t₂ = 15 s) · Distance = Area = ½vt₁ + vt₂
7. On a speed-time graph, a train accelerates uniformly from rest to 18 m/s in 8 s and then continues at a constant speed of 18 m/s for a further 12 s. Calculate the total distance travelled.
v_max = 18 m/s (t₁ = 8 s, t₂ = 12 s) · Distance = Area = ½vt₁ + vt₂
8. On a speed-time graph, a train accelerates uniformly from rest to 26 m/s in 11 s and then continues at a constant speed of 26 m/s for a further 19 s. Calculate the total distance travelled.
v_max = 26 m/s (t₁ = 11 s, t₂ = 19 s) · Distance = Area = ½vt₁ + vt₂
9. On a speed-time graph, a train accelerates uniformly from rest to 26 m/s in 7 s and then continues at a constant speed of 26 m/s for a further 15 s. Calculate the total distance travelled.
v_max = 26 m/s (t₁ = 7 s, t₂ = 15 s) · Distance = Area = ½vt₁ + vt₂
10. On a speed-time graph, a train accelerates uniformly from rest to 40 m/s in 10 s and then continues at a constant speed of 40 m/s for a further 10 s. Calculate the total distance travelled.
v_max = 40 m/s (t₁ = 10 s, t₂ = 10 s) · Distance = Area = ½vt₁ + vt₂
11. On a speed-time graph, a train accelerates uniformly from rest to 14 m/s in 10 s and then continues at a constant speed of 14 m/s for a further 17 s. Calculate the total distance travelled.
v_max = 14 m/s (t₁ = 10 s, t₂ = 17 s) · Distance = Area = ½vt₁ + vt₂
12. On a speed-time graph, a train accelerates uniformly from rest to 28 m/s in 4 s and then continues at a constant speed of 28 m/s for a further 7 s. Calculate the total distance travelled.
v_max = 28 m/s (t₁ = 4 s, t₂ = 7 s) · Distance = Area = ½vt₁ + vt₂

12 questions · Seed 52 · 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 18 m/s in 7 s and then continues at a constant speed of 18 m/s for a further 10 s. Calculate the total distance travelled.
243 m
Distance is the area under the speed-time graph: triangle area = ½ × 7 × 18 = 63 m, plus rectangle area = 10 × 18 = 180 m. Total distance = 63 + 180 = 243 m.
2. 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 4 s. Calculate the total distance travelled.
68 m
Distance is the area under the speed-time graph: triangle area = ½ × 9 × 8 = 36 m, plus rectangle area = 4 × 8 = 32 m. Total distance = 36 + 32 = 68 m.
3. On a speed-time graph, a train accelerates uniformly from rest to 28 m/s in 3 s and then continues at a constant speed of 28 m/s for a further 13 s. Calculate the total distance travelled.
406 m
Distance is the area under the speed-time graph: triangle area = ½ × 3 × 28 = 42 m, plus rectangle area = 13 × 28 = 364 m. Total distance = 42 + 364 = 406 m.
4. On a speed-time graph, a train accelerates uniformly from rest to 42 m/s in 3 s and then continues at a constant speed of 42 m/s for a further 8 s. Calculate the total distance travelled.
399 m
Distance is the area under the speed-time graph: triangle area = ½ × 3 × 42 = 63 m, plus rectangle area = 8 × 42 = 336 m. Total distance = 63 + 336 = 399 m.
5. On a speed-time graph, a train accelerates uniformly from rest to 10 m/s in 7 s and then continues at a constant speed of 10 m/s for a further 13 s. Calculate the total distance travelled.
165 m
Distance is the area under the speed-time graph: triangle area = ½ × 7 × 10 = 35 m, plus rectangle area = 13 × 10 = 130 m. Total distance = 35 + 130 = 165 m.
6. On a speed-time graph, a train accelerates uniformly from rest to 38 m/s in 9 s and then continues at a constant speed of 38 m/s for a further 15 s. Calculate the total distance travelled.
741 m
Distance is the area under the speed-time graph: triangle area = ½ × 9 × 38 = 171 m, plus rectangle area = 15 × 38 = 570 m. Total distance = 171 + 570 = 741 m.
7. On a speed-time graph, a train accelerates uniformly from rest to 18 m/s in 8 s and then continues at a constant speed of 18 m/s for a further 12 s. Calculate the total distance travelled.
288 m
Distance is the area under the speed-time graph: triangle area = ½ × 8 × 18 = 72 m, plus rectangle area = 12 × 18 = 216 m. Total distance = 72 + 216 = 288 m.
8. On a speed-time graph, a train accelerates uniformly from rest to 26 m/s in 11 s and then continues at a constant speed of 26 m/s for a further 19 s. Calculate the total distance travelled.
637 m
Distance is the area under the speed-time graph: triangle area = ½ × 11 × 26 = 143 m, plus rectangle area = 19 × 26 = 494 m. Total distance = 143 + 494 = 637 m.
9. On a speed-time graph, a train accelerates uniformly from rest to 26 m/s in 7 s and then continues at a constant speed of 26 m/s for a further 15 s. Calculate the total distance travelled.
481 m
Distance is the area under the speed-time graph: triangle area = ½ × 7 × 26 = 91 m, plus rectangle area = 15 × 26 = 390 m. Total distance = 91 + 390 = 481 m.
10. On a speed-time graph, a train accelerates uniformly from rest to 40 m/s in 10 s and then continues at a constant speed of 40 m/s for a further 10 s. Calculate the total distance travelled.
600 m
Distance is the area under the speed-time graph: triangle area = ½ × 10 × 40 = 200 m, plus rectangle area = 10 × 40 = 400 m. Total distance = 200 + 400 = 600 m.
11. On a speed-time graph, a train accelerates uniformly from rest to 14 m/s in 10 s and then continues at a constant speed of 14 m/s for a further 17 s. Calculate the total distance travelled.
308 m
Distance is the area under the speed-time graph: triangle area = ½ × 10 × 14 = 70 m, plus rectangle area = 17 × 14 = 238 m. Total distance = 70 + 238 = 308 m.
12. On a speed-time graph, a train accelerates uniformly from rest to 28 m/s in 4 s and then continues at a constant speed of 28 m/s for a further 7 s. Calculate the total distance travelled.
252 m
Distance is the area under the speed-time graph: triangle area = ½ × 4 × 28 = 56 m, plus rectangle area = 7 × 28 = 196 m. Total distance = 56 + 196 = 252 m.

12 questions · Seed 52 · Age guidance, not curriculum certification