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 46 m/s in 3 s and then continues at a constant speed of 46 m/s for a further 16 s. Calculate the total distance travelled.
v_max = 46 m/s (t₁ = 3 s, t₂ = 16 s) · Distance = Area = ½vt₁ + vt₂
2. 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 10 s. Calculate the total distance travelled.
v_max = 28 m/s (t₁ = 4 s, t₂ = 10 s) · Distance = Area = ½vt₁ + vt₂
3. 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
4. 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 6 s. Calculate the total distance travelled.
v_max = 50 m/s (t₁ = 10 s, t₂ = 6 s) · Distance = Area = ½vt₁ + vt₂
5. 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
6. On a speed-time graph, a train accelerates uniformly from rest to 34 m/s in 6 s and then continues at a constant speed of 34 m/s for a further 20 s. Calculate the total distance travelled.
v_max = 34 m/s (t₁ = 6 s, t₂ = 20 s) · Distance = Area = ½vt₁ + vt₂
7. On a speed-time graph, a train accelerates uniformly from rest to 28 m/s in 5 s and then continues at a constant speed of 28 m/s for a further 6 s. Calculate the total distance travelled.
v_max = 28 m/s (t₁ = 5 s, t₂ = 6 s) · Distance = Area = ½vt₁ + vt₂
8. On a speed-time graph, a train accelerates uniformly from rest to 48 m/s in 6 s and then continues at a constant speed of 48 m/s for a further 19 s. Calculate the total distance travelled.
v_max = 48 m/s (t₁ = 6 s, t₂ = 19 s) · Distance = Area = ½vt₁ + vt₂
9. On a speed-time graph, a train accelerates uniformly from rest to 42 m/s in 6 s and then continues at a constant speed of 42 m/s for a further 5 s. Calculate the total distance travelled.
v_max = 42 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 18 m/s in 6 s and then continues at a constant speed of 18 m/s for a further 11 s. Calculate the total distance travelled.
v_max = 18 m/s (t₁ = 6 s, t₂ = 11 s) · Distance = Area = ½vt₁ + vt₂
11. On a speed-time graph, a train accelerates uniformly from rest to 30 m/s in 5 s and then continues at a constant speed of 30 m/s for a further 9 s. Calculate the total distance travelled.
v_max = 30 m/s (t₁ = 5 s, t₂ = 9 s) · Distance = Area = ½vt₁ + vt₂
12. On a speed-time graph, a train accelerates uniformly from rest to 42 m/s in 4 s and then continues at a constant speed of 42 m/s for a further 18 s. Calculate the total distance travelled.
v_max = 42 m/s (t₁ = 4 s, t₂ = 18 s) · Distance = Area = ½vt₁ + vt₂

12 questions · Seed 104733 · 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 46 m/s in 3 s and then continues at a constant speed of 46 m/s for a further 16 s. Calculate the total distance travelled.
805 m
Distance is the area under the speed-time graph: triangle area = ½ × 3 × 46 = 69 m, plus rectangle area = 16 × 46 = 736 m. Total distance = 69 + 736 = 805 m.
2. 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 10 s. Calculate the total distance travelled.
336 m
Distance is the area under the speed-time graph: triangle area = ½ × 4 × 28 = 56 m, plus rectangle area = 10 × 28 = 280 m. Total distance = 56 + 280 = 336 m.
3. 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.
4. 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 6 s. Calculate the total distance travelled.
550 m
Distance is the area under the speed-time graph: triangle area = ½ × 10 × 50 = 250 m, plus rectangle area = 6 × 50 = 300 m. Total distance = 250 + 300 = 550 m.
5. 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.
6. On a speed-time graph, a train accelerates uniformly from rest to 34 m/s in 6 s and then continues at a constant speed of 34 m/s for a further 20 s. Calculate the total distance travelled.
782 m
Distance is the area under the speed-time graph: triangle area = ½ × 6 × 34 = 102 m, plus rectangle area = 20 × 34 = 680 m. Total distance = 102 + 680 = 782 m.
7. On a speed-time graph, a train accelerates uniformly from rest to 28 m/s in 5 s and then continues at a constant speed of 28 m/s for a further 6 s. Calculate the total distance travelled.
238 m
Distance is the area under the speed-time graph: triangle area = ½ × 5 × 28 = 70 m, plus rectangle area = 6 × 28 = 168 m. Total distance = 70 + 168 = 238 m.
8. On a speed-time graph, a train accelerates uniformly from rest to 48 m/s in 6 s and then continues at a constant speed of 48 m/s for a further 19 s. Calculate the total distance travelled.
1056 m
Distance is the area under the speed-time graph: triangle area = ½ × 6 × 48 = 144 m, plus rectangle area = 19 × 48 = 912 m. Total distance = 144 + 912 = 1056 m.
9. On a speed-time graph, a train accelerates uniformly from rest to 42 m/s in 6 s and then continues at a constant speed of 42 m/s for a further 5 s. Calculate the total distance travelled.
336 m
Distance is the area under the speed-time graph: triangle area = ½ × 6 × 42 = 126 m, plus rectangle area = 5 × 42 = 210 m. Total distance = 126 + 210 = 336 m.
10. On a speed-time graph, a train accelerates uniformly from rest to 18 m/s in 6 s and then continues at a constant speed of 18 m/s for a further 11 s. Calculate the total distance travelled.
252 m
Distance is the area under the speed-time graph: triangle area = ½ × 6 × 18 = 54 m, plus rectangle area = 11 × 18 = 198 m. Total distance = 54 + 198 = 252 m.
11. On a speed-time graph, a train accelerates uniformly from rest to 30 m/s in 5 s and then continues at a constant speed of 30 m/s for a further 9 s. Calculate the total distance travelled.
345 m
Distance is the area under the speed-time graph: triangle area = ½ × 5 × 30 = 75 m, plus rectangle area = 9 × 30 = 270 m. Total distance = 75 + 270 = 345 m.
12. On a speed-time graph, a train accelerates uniformly from rest to 42 m/s in 4 s and then continues at a constant speed of 42 m/s for a further 18 s. Calculate the total distance travelled.
840 m
Distance is the area under the speed-time graph: triangle area = ½ × 4 × 42 = 84 m, plus rectangle area = 18 × 42 = 756 m. Total distance = 84 + 756 = 840 m.

12 questions · Seed 104733 · 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 46 m/s in 3 s and then continues at a constant speed of 46 m/s for a further 16 s. Calculate the total distance travelled.
v_max = 46 m/s (t₁ = 3 s, t₂ = 16 s) · Distance = Area = ½vt₁ + vt₂
2. 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 10 s. Calculate the total distance travelled.
v_max = 28 m/s (t₁ = 4 s, t₂ = 10 s) · Distance = Area = ½vt₁ + vt₂
3. 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
4. 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 6 s. Calculate the total distance travelled.
v_max = 50 m/s (t₁ = 10 s, t₂ = 6 s) · Distance = Area = ½vt₁ + vt₂
5. 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
6. On a speed-time graph, a train accelerates uniformly from rest to 34 m/s in 6 s and then continues at a constant speed of 34 m/s for a further 20 s. Calculate the total distance travelled.
v_max = 34 m/s (t₁ = 6 s, t₂ = 20 s) · Distance = Area = ½vt₁ + vt₂
7. On a speed-time graph, a train accelerates uniformly from rest to 28 m/s in 5 s and then continues at a constant speed of 28 m/s for a further 6 s. Calculate the total distance travelled.
v_max = 28 m/s (t₁ = 5 s, t₂ = 6 s) · Distance = Area = ½vt₁ + vt₂
8. On a speed-time graph, a train accelerates uniformly from rest to 48 m/s in 6 s and then continues at a constant speed of 48 m/s for a further 19 s. Calculate the total distance travelled.
v_max = 48 m/s (t₁ = 6 s, t₂ = 19 s) · Distance = Area = ½vt₁ + vt₂
9. On a speed-time graph, a train accelerates uniformly from rest to 42 m/s in 6 s and then continues at a constant speed of 42 m/s for a further 5 s. Calculate the total distance travelled.
v_max = 42 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 18 m/s in 6 s and then continues at a constant speed of 18 m/s for a further 11 s. Calculate the total distance travelled.
v_max = 18 m/s (t₁ = 6 s, t₂ = 11 s) · Distance = Area = ½vt₁ + vt₂
11. On a speed-time graph, a train accelerates uniformly from rest to 30 m/s in 5 s and then continues at a constant speed of 30 m/s for a further 9 s. Calculate the total distance travelled.
v_max = 30 m/s (t₁ = 5 s, t₂ = 9 s) · Distance = Area = ½vt₁ + vt₂
12. On a speed-time graph, a train accelerates uniformly from rest to 42 m/s in 4 s and then continues at a constant speed of 42 m/s for a further 18 s. Calculate the total distance travelled.
v_max = 42 m/s (t₁ = 4 s, t₂ = 18 s) · Distance = Area = ½vt₁ + vt₂

12 questions · Seed 104733 · 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 46 m/s in 3 s and then continues at a constant speed of 46 m/s for a further 16 s. Calculate the total distance travelled.
805 m
Distance is the area under the speed-time graph: triangle area = ½ × 3 × 46 = 69 m, plus rectangle area = 16 × 46 = 736 m. Total distance = 69 + 736 = 805 m.
2. 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 10 s. Calculate the total distance travelled.
336 m
Distance is the area under the speed-time graph: triangle area = ½ × 4 × 28 = 56 m, plus rectangle area = 10 × 28 = 280 m. Total distance = 56 + 280 = 336 m.
3. 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.
4. 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 6 s. Calculate the total distance travelled.
550 m
Distance is the area under the speed-time graph: triangle area = ½ × 10 × 50 = 250 m, plus rectangle area = 6 × 50 = 300 m. Total distance = 250 + 300 = 550 m.
5. 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.
6. On a speed-time graph, a train accelerates uniformly from rest to 34 m/s in 6 s and then continues at a constant speed of 34 m/s for a further 20 s. Calculate the total distance travelled.
782 m
Distance is the area under the speed-time graph: triangle area = ½ × 6 × 34 = 102 m, plus rectangle area = 20 × 34 = 680 m. Total distance = 102 + 680 = 782 m.
7. On a speed-time graph, a train accelerates uniformly from rest to 28 m/s in 5 s and then continues at a constant speed of 28 m/s for a further 6 s. Calculate the total distance travelled.
238 m
Distance is the area under the speed-time graph: triangle area = ½ × 5 × 28 = 70 m, plus rectangle area = 6 × 28 = 168 m. Total distance = 70 + 168 = 238 m.
8. On a speed-time graph, a train accelerates uniformly from rest to 48 m/s in 6 s and then continues at a constant speed of 48 m/s for a further 19 s. Calculate the total distance travelled.
1056 m
Distance is the area under the speed-time graph: triangle area = ½ × 6 × 48 = 144 m, plus rectangle area = 19 × 48 = 912 m. Total distance = 144 + 912 = 1056 m.
9. On a speed-time graph, a train accelerates uniformly from rest to 42 m/s in 6 s and then continues at a constant speed of 42 m/s for a further 5 s. Calculate the total distance travelled.
336 m
Distance is the area under the speed-time graph: triangle area = ½ × 6 × 42 = 126 m, plus rectangle area = 5 × 42 = 210 m. Total distance = 126 + 210 = 336 m.
10. On a speed-time graph, a train accelerates uniformly from rest to 18 m/s in 6 s and then continues at a constant speed of 18 m/s for a further 11 s. Calculate the total distance travelled.
252 m
Distance is the area under the speed-time graph: triangle area = ½ × 6 × 18 = 54 m, plus rectangle area = 11 × 18 = 198 m. Total distance = 54 + 198 = 252 m.
11. On a speed-time graph, a train accelerates uniformly from rest to 30 m/s in 5 s and then continues at a constant speed of 30 m/s for a further 9 s. Calculate the total distance travelled.
345 m
Distance is the area under the speed-time graph: triangle area = ½ × 5 × 30 = 75 m, plus rectangle area = 9 × 30 = 270 m. Total distance = 75 + 270 = 345 m.
12. On a speed-time graph, a train accelerates uniformly from rest to 42 m/s in 4 s and then continues at a constant speed of 42 m/s for a further 18 s. Calculate the total distance travelled.
840 m
Distance is the area under the speed-time graph: triangle area = ½ × 4 × 42 = 84 m, plus rectangle area = 18 × 42 = 756 m. Total distance = 84 + 756 = 840 m.

12 questions · Seed 104733 · Age guidance, not curriculum certification