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 36 m/s in 8 s and then continues at a constant speed of 36 m/s for a further 5 s. Calculate the total distance travelled.
v_max = 36 m/s (t₁ = 8 s, t₂ = 5 s) · Distance = Area = ½vt₁ + vt₂
2. On a speed-time graph, a train accelerates uniformly from rest to 10 m/s in 4 s and then continues at a constant speed of 10 m/s for a further 6 s. Calculate the total distance travelled.
v_max = 10 m/s (t₁ = 4 s, t₂ = 6 s) · Distance = Area = ½vt₁ + vt₂
3. 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 7 s. Calculate the total distance travelled.
v_max = 26 m/s (t₁ = 6 s, t₂ = 7 s) · Distance = Area = ½vt₁ + vt₂
4. On a speed-time graph, a train accelerates uniformly from rest to 10 m/s in 2 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 = 2 s, t₂ = 13 s) · Distance = Area = ½vt₁ + vt₂
5. On a speed-time graph, a train accelerates uniformly from rest to 46 m/s in 5 s and then continues at a constant speed of 46 m/s for a further 4 s. Calculate the total distance travelled.
v_max = 46 m/s (t₁ = 5 s, t₂ = 4 s) · Distance = Area = ½vt₁ + vt₂
6. On a speed-time graph, a train accelerates uniformly from rest to 34 m/s in 3 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 = 3 s, t₂ = 11 s) · Distance = Area = ½vt₁ + vt₂
7. On a speed-time graph, a train accelerates uniformly from rest to 32 m/s in 8 s and then continues at a constant speed of 32 m/s for a further 17 s. Calculate the total distance travelled.
v_max = 32 m/s (t₁ = 8 s, t₂ = 17 s) · Distance = Area = ½vt₁ + vt₂
8. On a speed-time graph, a train accelerates uniformly from rest to 30 m/s in 4 s and then continues at a constant speed of 30 m/s for a further 14 s. Calculate the total distance travelled.
v_max = 30 m/s (t₁ = 4 s, t₂ = 14 s) · Distance = Area = ½vt₁ + vt₂
9. On a speed-time graph, a train accelerates uniformly from rest to 10 m/s in 2 s and then continues at a constant speed of 10 m/s for a further 5 s. Calculate the total distance travelled.
v_max = 10 m/s (t₁ = 2 s, t₂ = 5 s) · Distance = Area = ½vt₁ + vt₂
10. On a speed-time graph, a train accelerates uniformly from rest to 50 m/s in 12 s and then continues at a constant speed of 50 m/s for a further 4 s. Calculate the total distance travelled.
v_max = 50 m/s (t₁ = 12 s, t₂ = 4 s) · Distance = Area = ½vt₁ + vt₂
11. 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 16 s. Calculate the total distance travelled.
v_max = 32 m/s (t₁ = 6 s, t₂ = 16 s) · Distance = Area = ½vt₁ + vt₂
12. On a speed-time graph, a train accelerates uniformly from rest to 8 m/s in 8 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 = 8 s, t₂ = 12 s) · Distance = Area = ½vt₁ + vt₂

12 questions · Seed 104739 · 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 36 m/s in 8 s and then continues at a constant speed of 36 m/s for a further 5 s. Calculate the total distance travelled.
324 m
Distance is the area under the speed-time graph: triangle area = ½ × 8 × 36 = 144 m, plus rectangle area = 5 × 36 = 180 m. Total distance = 144 + 180 = 324 m.
2. On a speed-time graph, a train accelerates uniformly from rest to 10 m/s in 4 s and then continues at a constant speed of 10 m/s for a further 6 s. Calculate the total distance travelled.
80 m
Distance is the area under the speed-time graph: triangle area = ½ × 4 × 10 = 20 m, plus rectangle area = 6 × 10 = 60 m. Total distance = 20 + 60 = 80 m.
3. 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 7 s. Calculate the total distance travelled.
260 m
Distance is the area under the speed-time graph: triangle area = ½ × 6 × 26 = 78 m, plus rectangle area = 7 × 26 = 182 m. Total distance = 78 + 182 = 260 m.
4. On a speed-time graph, a train accelerates uniformly from rest to 10 m/s in 2 s and then continues at a constant speed of 10 m/s for a further 13 s. Calculate the total distance travelled.
140 m
Distance is the area under the speed-time graph: triangle area = ½ × 2 × 10 = 10 m, plus rectangle area = 13 × 10 = 130 m. Total distance = 10 + 130 = 140 m.
5. On a speed-time graph, a train accelerates uniformly from rest to 46 m/s in 5 s and then continues at a constant speed of 46 m/s for a further 4 s. Calculate the total distance travelled.
299 m
Distance is the area under the speed-time graph: triangle area = ½ × 5 × 46 = 115 m, plus rectangle area = 4 × 46 = 184 m. Total distance = 115 + 184 = 299 m.
6. On a speed-time graph, a train accelerates uniformly from rest to 34 m/s in 3 s and then continues at a constant speed of 34 m/s for a further 11 s. Calculate the total distance travelled.
425 m
Distance is the area under the speed-time graph: triangle area = ½ × 3 × 34 = 51 m, plus rectangle area = 11 × 34 = 374 m. Total distance = 51 + 374 = 425 m.
7. On a speed-time graph, a train accelerates uniformly from rest to 32 m/s in 8 s and then continues at a constant speed of 32 m/s for a further 17 s. Calculate the total distance travelled.
672 m
Distance is the area under the speed-time graph: triangle area = ½ × 8 × 32 = 128 m, plus rectangle area = 17 × 32 = 544 m. Total distance = 128 + 544 = 672 m.
8. On a speed-time graph, a train accelerates uniformly from rest to 30 m/s in 4 s and then continues at a constant speed of 30 m/s for a further 14 s. Calculate the total distance travelled.
480 m
Distance is the area under the speed-time graph: triangle area = ½ × 4 × 30 = 60 m, plus rectangle area = 14 × 30 = 420 m. Total distance = 60 + 420 = 480 m.
9. On a speed-time graph, a train accelerates uniformly from rest to 10 m/s in 2 s and then continues at a constant speed of 10 m/s for a further 5 s. Calculate the total distance travelled.
60 m
Distance is the area under the speed-time graph: triangle area = ½ × 2 × 10 = 10 m, plus rectangle area = 5 × 10 = 50 m. Total distance = 10 + 50 = 60 m.
10. On a speed-time graph, a train accelerates uniformly from rest to 50 m/s in 12 s and then continues at a constant speed of 50 m/s for a further 4 s. Calculate the total distance travelled.
500 m
Distance is the area under the speed-time graph: triangle area = ½ × 12 × 50 = 300 m, plus rectangle area = 4 × 50 = 200 m. Total distance = 300 + 200 = 500 m.
11. 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 16 s. Calculate the total distance travelled.
608 m
Distance is the area under the speed-time graph: triangle area = ½ × 6 × 32 = 96 m, plus rectangle area = 16 × 32 = 512 m. Total distance = 96 + 512 = 608 m.
12. On a speed-time graph, a train accelerates uniformly from rest to 8 m/s in 8 s and then continues at a constant speed of 8 m/s for a further 12 s. Calculate the total distance travelled.
128 m
Distance is the area under the speed-time graph: triangle area = ½ × 8 × 8 = 32 m, plus rectangle area = 12 × 8 = 96 m. Total distance = 32 + 96 = 128 m.

12 questions · Seed 104739 · 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 36 m/s in 8 s and then continues at a constant speed of 36 m/s for a further 5 s. Calculate the total distance travelled.
v_max = 36 m/s (t₁ = 8 s, t₂ = 5 s) · Distance = Area = ½vt₁ + vt₂
2. On a speed-time graph, a train accelerates uniformly from rest to 10 m/s in 4 s and then continues at a constant speed of 10 m/s for a further 6 s. Calculate the total distance travelled.
v_max = 10 m/s (t₁ = 4 s, t₂ = 6 s) · Distance = Area = ½vt₁ + vt₂
3. 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 7 s. Calculate the total distance travelled.
v_max = 26 m/s (t₁ = 6 s, t₂ = 7 s) · Distance = Area = ½vt₁ + vt₂
4. On a speed-time graph, a train accelerates uniformly from rest to 10 m/s in 2 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 = 2 s, t₂ = 13 s) · Distance = Area = ½vt₁ + vt₂
5. On a speed-time graph, a train accelerates uniformly from rest to 46 m/s in 5 s and then continues at a constant speed of 46 m/s for a further 4 s. Calculate the total distance travelled.
v_max = 46 m/s (t₁ = 5 s, t₂ = 4 s) · Distance = Area = ½vt₁ + vt₂
6. On a speed-time graph, a train accelerates uniformly from rest to 34 m/s in 3 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 = 3 s, t₂ = 11 s) · Distance = Area = ½vt₁ + vt₂
7. On a speed-time graph, a train accelerates uniformly from rest to 32 m/s in 8 s and then continues at a constant speed of 32 m/s for a further 17 s. Calculate the total distance travelled.
v_max = 32 m/s (t₁ = 8 s, t₂ = 17 s) · Distance = Area = ½vt₁ + vt₂
8. On a speed-time graph, a train accelerates uniformly from rest to 30 m/s in 4 s and then continues at a constant speed of 30 m/s for a further 14 s. Calculate the total distance travelled.
v_max = 30 m/s (t₁ = 4 s, t₂ = 14 s) · Distance = Area = ½vt₁ + vt₂
9. On a speed-time graph, a train accelerates uniformly from rest to 10 m/s in 2 s and then continues at a constant speed of 10 m/s for a further 5 s. Calculate the total distance travelled.
v_max = 10 m/s (t₁ = 2 s, t₂ = 5 s) · Distance = Area = ½vt₁ + vt₂
10. On a speed-time graph, a train accelerates uniformly from rest to 50 m/s in 12 s and then continues at a constant speed of 50 m/s for a further 4 s. Calculate the total distance travelled.
v_max = 50 m/s (t₁ = 12 s, t₂ = 4 s) · Distance = Area = ½vt₁ + vt₂
11. 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 16 s. Calculate the total distance travelled.
v_max = 32 m/s (t₁ = 6 s, t₂ = 16 s) · Distance = Area = ½vt₁ + vt₂
12. On a speed-time graph, a train accelerates uniformly from rest to 8 m/s in 8 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 = 8 s, t₂ = 12 s) · Distance = Area = ½vt₁ + vt₂

12 questions · Seed 104739 · 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 36 m/s in 8 s and then continues at a constant speed of 36 m/s for a further 5 s. Calculate the total distance travelled.
324 m
Distance is the area under the speed-time graph: triangle area = ½ × 8 × 36 = 144 m, plus rectangle area = 5 × 36 = 180 m. Total distance = 144 + 180 = 324 m.
2. On a speed-time graph, a train accelerates uniformly from rest to 10 m/s in 4 s and then continues at a constant speed of 10 m/s for a further 6 s. Calculate the total distance travelled.
80 m
Distance is the area under the speed-time graph: triangle area = ½ × 4 × 10 = 20 m, plus rectangle area = 6 × 10 = 60 m. Total distance = 20 + 60 = 80 m.
3. 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 7 s. Calculate the total distance travelled.
260 m
Distance is the area under the speed-time graph: triangle area = ½ × 6 × 26 = 78 m, plus rectangle area = 7 × 26 = 182 m. Total distance = 78 + 182 = 260 m.
4. On a speed-time graph, a train accelerates uniformly from rest to 10 m/s in 2 s and then continues at a constant speed of 10 m/s for a further 13 s. Calculate the total distance travelled.
140 m
Distance is the area under the speed-time graph: triangle area = ½ × 2 × 10 = 10 m, plus rectangle area = 13 × 10 = 130 m. Total distance = 10 + 130 = 140 m.
5. On a speed-time graph, a train accelerates uniformly from rest to 46 m/s in 5 s and then continues at a constant speed of 46 m/s for a further 4 s. Calculate the total distance travelled.
299 m
Distance is the area under the speed-time graph: triangle area = ½ × 5 × 46 = 115 m, plus rectangle area = 4 × 46 = 184 m. Total distance = 115 + 184 = 299 m.
6. On a speed-time graph, a train accelerates uniformly from rest to 34 m/s in 3 s and then continues at a constant speed of 34 m/s for a further 11 s. Calculate the total distance travelled.
425 m
Distance is the area under the speed-time graph: triangle area = ½ × 3 × 34 = 51 m, plus rectangle area = 11 × 34 = 374 m. Total distance = 51 + 374 = 425 m.
7. On a speed-time graph, a train accelerates uniformly from rest to 32 m/s in 8 s and then continues at a constant speed of 32 m/s for a further 17 s. Calculate the total distance travelled.
672 m
Distance is the area under the speed-time graph: triangle area = ½ × 8 × 32 = 128 m, plus rectangle area = 17 × 32 = 544 m. Total distance = 128 + 544 = 672 m.
8. On a speed-time graph, a train accelerates uniformly from rest to 30 m/s in 4 s and then continues at a constant speed of 30 m/s for a further 14 s. Calculate the total distance travelled.
480 m
Distance is the area under the speed-time graph: triangle area = ½ × 4 × 30 = 60 m, plus rectangle area = 14 × 30 = 420 m. Total distance = 60 + 420 = 480 m.
9. On a speed-time graph, a train accelerates uniformly from rest to 10 m/s in 2 s and then continues at a constant speed of 10 m/s for a further 5 s. Calculate the total distance travelled.
60 m
Distance is the area under the speed-time graph: triangle area = ½ × 2 × 10 = 10 m, plus rectangle area = 5 × 10 = 50 m. Total distance = 10 + 50 = 60 m.
10. On a speed-time graph, a train accelerates uniformly from rest to 50 m/s in 12 s and then continues at a constant speed of 50 m/s for a further 4 s. Calculate the total distance travelled.
500 m
Distance is the area under the speed-time graph: triangle area = ½ × 12 × 50 = 300 m, plus rectangle area = 4 × 50 = 200 m. Total distance = 300 + 200 = 500 m.
11. 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 16 s. Calculate the total distance travelled.
608 m
Distance is the area under the speed-time graph: triangle area = ½ × 6 × 32 = 96 m, plus rectangle area = 16 × 32 = 512 m. Total distance = 96 + 512 = 608 m.
12. On a speed-time graph, a train accelerates uniformly from rest to 8 m/s in 8 s and then continues at a constant speed of 8 m/s for a further 12 s. Calculate the total distance travelled.
128 m
Distance is the area under the speed-time graph: triangle area = ½ × 8 × 8 = 32 m, plus rectangle area = 12 × 8 = 96 m. Total distance = 32 + 96 = 128 m.

12 questions · Seed 104739 · Age guidance, not curriculum certification