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 8 m/s in 6 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 = 6 s, t₂ = 18 s) · Distance = Area = ½vt₁ + vt₂
2. On a speed-time graph, a train accelerates uniformly from rest to 26 m/s in 4 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 = 4 s, t₂ = 5 s) · Distance = Area = ½vt₁ + vt₂
3. On a speed-time graph, a train accelerates uniformly from rest to 32 m/s in 7 s and then continues at a constant speed of 32 m/s for a further 6 s. Calculate the total distance travelled.
v_max = 32 m/s (t₁ = 7 s, t₂ = 6 s) · Distance = Area = ½vt₁ + vt₂
4. On a speed-time graph, a train accelerates uniformly from rest to 46 m/s in 10 s and then continues at a constant speed of 46 m/s for a further 15 s. Calculate the total distance travelled.
v_max = 46 m/s (t₁ = 10 s, t₂ = 15 s) · Distance = Area = ½vt₁ + vt₂
5. On a speed-time graph, a train accelerates uniformly from rest to 26 m/s in 10 s and then continues at a constant speed of 26 m/s for a further 10 s. Calculate the total distance travelled.
v_max = 26 m/s (t₁ = 10 s, t₂ = 10 s) · Distance = Area = ½vt₁ + vt₂
6. On a speed-time graph, a train accelerates uniformly from rest to 18 m/s in 2 s and then continues at a constant speed of 18 m/s for a further 14 s. Calculate the total distance travelled.
v_max = 18 m/s (t₁ = 2 s, t₂ = 14 s) · Distance = Area = ½vt₁ + vt₂
7. On a speed-time graph, a train accelerates uniformly from rest to 40 m/s in 6 s and then continues at a constant speed of 40 m/s for a further 16 s. Calculate the total distance travelled.
v_max = 40 m/s (t₁ = 6 s, t₂ = 16 s) · Distance = Area = ½vt₁ + vt₂
8. On a speed-time graph, a train accelerates uniformly from rest to 16 m/s in 9 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 = 9 s, t₂ = 12 s) · Distance = Area = ½vt₁ + vt₂
9. On a speed-time graph, a train accelerates uniformly from rest to 26 m/s in 6 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 = 6 s, t₂ = 5 s) · Distance = Area = ½vt₁ + vt₂
10. On a speed-time graph, a train accelerates uniformly from rest to 48 m/s in 8 s and then continues at a constant speed of 48 m/s for a further 10 s. Calculate the total distance travelled.
v_max = 48 m/s (t₁ = 8 s, t₂ = 10 s) · Distance = Area = ½vt₁ + vt₂
11. 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
12. On a speed-time graph, a train accelerates uniformly from rest to 34 m/s in 4 s and then continues at a constant speed of 34 m/s for a further 6 s. Calculate the total distance travelled.
v_max = 34 m/s (t₁ = 4 s, t₂ = 6 s) · Distance = Area = ½vt₁ + vt₂

12 questions · Seed 48 · 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 6 s and then continues at a constant speed of 8 m/s for a further 18 s. Calculate the total distance travelled.
168 m
Distance is the area under the speed-time graph: triangle area = ½ × 6 × 8 = 24 m, plus rectangle area = 18 × 8 = 144 m. Total distance = 24 + 144 = 168 m.
2. On a speed-time graph, a train accelerates uniformly from rest to 26 m/s in 4 s and then continues at a constant speed of 26 m/s for a further 5 s. Calculate the total distance travelled.
182 m
Distance is the area under the speed-time graph: triangle area = ½ × 4 × 26 = 52 m, plus rectangle area = 5 × 26 = 130 m. Total distance = 52 + 130 = 182 m.
3. On a speed-time graph, a train accelerates uniformly from rest to 32 m/s in 7 s and then continues at a constant speed of 32 m/s for a further 6 s. Calculate the total distance travelled.
304 m
Distance is the area under the speed-time graph: triangle area = ½ × 7 × 32 = 112 m, plus rectangle area = 6 × 32 = 192 m. Total distance = 112 + 192 = 304 m.
4. On a speed-time graph, a train accelerates uniformly from rest to 46 m/s in 10 s and then continues at a constant speed of 46 m/s for a further 15 s. Calculate the total distance travelled.
920 m
Distance is the area under the speed-time graph: triangle area = ½ × 10 × 46 = 230 m, plus rectangle area = 15 × 46 = 690 m. Total distance = 230 + 690 = 920 m.
5. On a speed-time graph, a train accelerates uniformly from rest to 26 m/s in 10 s and then continues at a constant speed of 26 m/s for a further 10 s. Calculate the total distance travelled.
390 m
Distance is the area under the speed-time graph: triangle area = ½ × 10 × 26 = 130 m, plus rectangle area = 10 × 26 = 260 m. Total distance = 130 + 260 = 390 m.
6. On a speed-time graph, a train accelerates uniformly from rest to 18 m/s in 2 s and then continues at a constant speed of 18 m/s for a further 14 s. Calculate the total distance travelled.
270 m
Distance is the area under the speed-time graph: triangle area = ½ × 2 × 18 = 18 m, plus rectangle area = 14 × 18 = 252 m. Total distance = 18 + 252 = 270 m.
7. On a speed-time graph, a train accelerates uniformly from rest to 40 m/s in 6 s and then continues at a constant speed of 40 m/s for a further 16 s. Calculate the total distance travelled.
760 m
Distance is the area under the speed-time graph: triangle area = ½ × 6 × 40 = 120 m, plus rectangle area = 16 × 40 = 640 m. Total distance = 120 + 640 = 760 m.
8. On a speed-time graph, a train accelerates uniformly from rest to 16 m/s in 9 s and then continues at a constant speed of 16 m/s for a further 12 s. Calculate the total distance travelled.
264 m
Distance is the area under the speed-time graph: triangle area = ½ × 9 × 16 = 72 m, plus rectangle area = 12 × 16 = 192 m. Total distance = 72 + 192 = 264 m.
9. On a speed-time graph, a train accelerates uniformly from rest to 26 m/s in 6 s and then continues at a constant speed of 26 m/s for a further 5 s. Calculate the total distance travelled.
208 m
Distance is the area under the speed-time graph: triangle area = ½ × 6 × 26 = 78 m, plus rectangle area = 5 × 26 = 130 m. Total distance = 78 + 130 = 208 m.
10. On a speed-time graph, a train accelerates uniformly from rest to 48 m/s in 8 s and then continues at a constant speed of 48 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 × 8 × 48 = 192 m, plus rectangle area = 10 × 48 = 480 m. Total distance = 192 + 480 = 672 m.
11. 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.
12. On a speed-time graph, a train accelerates uniformly from rest to 34 m/s in 4 s and then continues at a constant speed of 34 m/s for a further 6 s. Calculate the total distance travelled.
272 m
Distance is the area under the speed-time graph: triangle area = ½ × 4 × 34 = 68 m, plus rectangle area = 6 × 34 = 204 m. Total distance = 68 + 204 = 272 m.

12 questions · Seed 48 · 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 6 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 = 6 s, t₂ = 18 s) · Distance = Area = ½vt₁ + vt₂
2. On a speed-time graph, a train accelerates uniformly from rest to 26 m/s in 4 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 = 4 s, t₂ = 5 s) · Distance = Area = ½vt₁ + vt₂
3. On a speed-time graph, a train accelerates uniformly from rest to 32 m/s in 7 s and then continues at a constant speed of 32 m/s for a further 6 s. Calculate the total distance travelled.
v_max = 32 m/s (t₁ = 7 s, t₂ = 6 s) · Distance = Area = ½vt₁ + vt₂
4. On a speed-time graph, a train accelerates uniformly from rest to 46 m/s in 10 s and then continues at a constant speed of 46 m/s for a further 15 s. Calculate the total distance travelled.
v_max = 46 m/s (t₁ = 10 s, t₂ = 15 s) · Distance = Area = ½vt₁ + vt₂
5. On a speed-time graph, a train accelerates uniformly from rest to 26 m/s in 10 s and then continues at a constant speed of 26 m/s for a further 10 s. Calculate the total distance travelled.
v_max = 26 m/s (t₁ = 10 s, t₂ = 10 s) · Distance = Area = ½vt₁ + vt₂
6. On a speed-time graph, a train accelerates uniformly from rest to 18 m/s in 2 s and then continues at a constant speed of 18 m/s for a further 14 s. Calculate the total distance travelled.
v_max = 18 m/s (t₁ = 2 s, t₂ = 14 s) · Distance = Area = ½vt₁ + vt₂
7. On a speed-time graph, a train accelerates uniformly from rest to 40 m/s in 6 s and then continues at a constant speed of 40 m/s for a further 16 s. Calculate the total distance travelled.
v_max = 40 m/s (t₁ = 6 s, t₂ = 16 s) · Distance = Area = ½vt₁ + vt₂
8. On a speed-time graph, a train accelerates uniformly from rest to 16 m/s in 9 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 = 9 s, t₂ = 12 s) · Distance = Area = ½vt₁ + vt₂
9. On a speed-time graph, a train accelerates uniformly from rest to 26 m/s in 6 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 = 6 s, t₂ = 5 s) · Distance = Area = ½vt₁ + vt₂
10. On a speed-time graph, a train accelerates uniformly from rest to 48 m/s in 8 s and then continues at a constant speed of 48 m/s for a further 10 s. Calculate the total distance travelled.
v_max = 48 m/s (t₁ = 8 s, t₂ = 10 s) · Distance = Area = ½vt₁ + vt₂
11. 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
12. On a speed-time graph, a train accelerates uniformly from rest to 34 m/s in 4 s and then continues at a constant speed of 34 m/s for a further 6 s. Calculate the total distance travelled.
v_max = 34 m/s (t₁ = 4 s, t₂ = 6 s) · Distance = Area = ½vt₁ + vt₂

12 questions · Seed 48 · 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 6 s and then continues at a constant speed of 8 m/s for a further 18 s. Calculate the total distance travelled.
168 m
Distance is the area under the speed-time graph: triangle area = ½ × 6 × 8 = 24 m, plus rectangle area = 18 × 8 = 144 m. Total distance = 24 + 144 = 168 m.
2. On a speed-time graph, a train accelerates uniformly from rest to 26 m/s in 4 s and then continues at a constant speed of 26 m/s for a further 5 s. Calculate the total distance travelled.
182 m
Distance is the area under the speed-time graph: triangle area = ½ × 4 × 26 = 52 m, plus rectangle area = 5 × 26 = 130 m. Total distance = 52 + 130 = 182 m.
3. On a speed-time graph, a train accelerates uniformly from rest to 32 m/s in 7 s and then continues at a constant speed of 32 m/s for a further 6 s. Calculate the total distance travelled.
304 m
Distance is the area under the speed-time graph: triangle area = ½ × 7 × 32 = 112 m, plus rectangle area = 6 × 32 = 192 m. Total distance = 112 + 192 = 304 m.
4. On a speed-time graph, a train accelerates uniformly from rest to 46 m/s in 10 s and then continues at a constant speed of 46 m/s for a further 15 s. Calculate the total distance travelled.
920 m
Distance is the area under the speed-time graph: triangle area = ½ × 10 × 46 = 230 m, plus rectangle area = 15 × 46 = 690 m. Total distance = 230 + 690 = 920 m.
5. On a speed-time graph, a train accelerates uniformly from rest to 26 m/s in 10 s and then continues at a constant speed of 26 m/s for a further 10 s. Calculate the total distance travelled.
390 m
Distance is the area under the speed-time graph: triangle area = ½ × 10 × 26 = 130 m, plus rectangle area = 10 × 26 = 260 m. Total distance = 130 + 260 = 390 m.
6. On a speed-time graph, a train accelerates uniformly from rest to 18 m/s in 2 s and then continues at a constant speed of 18 m/s for a further 14 s. Calculate the total distance travelled.
270 m
Distance is the area under the speed-time graph: triangle area = ½ × 2 × 18 = 18 m, plus rectangle area = 14 × 18 = 252 m. Total distance = 18 + 252 = 270 m.
7. On a speed-time graph, a train accelerates uniformly from rest to 40 m/s in 6 s and then continues at a constant speed of 40 m/s for a further 16 s. Calculate the total distance travelled.
760 m
Distance is the area under the speed-time graph: triangle area = ½ × 6 × 40 = 120 m, plus rectangle area = 16 × 40 = 640 m. Total distance = 120 + 640 = 760 m.
8. On a speed-time graph, a train accelerates uniformly from rest to 16 m/s in 9 s and then continues at a constant speed of 16 m/s for a further 12 s. Calculate the total distance travelled.
264 m
Distance is the area under the speed-time graph: triangle area = ½ × 9 × 16 = 72 m, plus rectangle area = 12 × 16 = 192 m. Total distance = 72 + 192 = 264 m.
9. On a speed-time graph, a train accelerates uniformly from rest to 26 m/s in 6 s and then continues at a constant speed of 26 m/s for a further 5 s. Calculate the total distance travelled.
208 m
Distance is the area under the speed-time graph: triangle area = ½ × 6 × 26 = 78 m, plus rectangle area = 5 × 26 = 130 m. Total distance = 78 + 130 = 208 m.
10. On a speed-time graph, a train accelerates uniformly from rest to 48 m/s in 8 s and then continues at a constant speed of 48 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 × 8 × 48 = 192 m, plus rectangle area = 10 × 48 = 480 m. Total distance = 192 + 480 = 672 m.
11. 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.
12. On a speed-time graph, a train accelerates uniformly from rest to 34 m/s in 4 s and then continues at a constant speed of 34 m/s for a further 6 s. Calculate the total distance travelled.
272 m
Distance is the area under the speed-time graph: triangle area = ½ × 4 × 34 = 68 m, plus rectangle area = 6 × 34 = 204 m. Total distance = 68 + 204 = 272 m.

12 questions · Seed 48 · Age guidance, not curriculum certification