ScienceAges 16-18

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 16-18

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 4 s and then continues at a constant speed of 18 m/s for a further 15 s. Calculate the total distance travelled.
v_max = 18 m/s (t₁ = 4 s, t₂ = 15 s) · Distance = Area = ½vt₁ + vt₂
2. 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 15 s. Calculate the total distance travelled.
v_max = 8 m/s (t₁ = 6 s, t₂ = 15 s) · Distance = Area = ½vt₁ + vt₂
3. On a speed-time graph, a train accelerates uniformly from rest to 12 m/s in 8 s and then continues at a constant speed of 12 m/s for a further 14 s. Calculate the total distance travelled.
v_max = 12 m/s (t₁ = 8 s, t₂ = 14 s) · Distance = Area = ½vt₁ + vt₂
4. 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 10 s. Calculate the total distance travelled.
v_max = 10 m/s (t₁ = 4 s, t₂ = 10 s) · Distance = Area = ½vt₁ + vt₂
5. On a speed-time graph, a train accelerates uniformly from rest to 12 m/s in 8 s and then continues at a constant speed of 12 m/s for a further 5 s. Calculate the total distance travelled.
v_max = 12 m/s (t₁ = 8 s, t₂ = 5 s) · Distance = Area = ½vt₁ + vt₂
6. On a speed-time graph, a train accelerates uniformly from rest to 24 m/s in 6 s and then continues at a constant speed of 24 m/s for a further 5 s. Calculate the total distance travelled.
v_max = 24 m/s (t₁ = 6 s, t₂ = 5 s) · Distance = Area = ½vt₁ + vt₂
7. On a speed-time graph, a train accelerates uniformly from rest to 28 m/s in 10 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 = 10 s, t₂ = 10 s) · Distance = Area = ½vt₁ + vt₂
8. 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 5 s. Calculate the total distance travelled.
v_max = 28 m/s (t₁ = 3 s, t₂ = 5 s) · Distance = Area = ½vt₁ + vt₂
9. 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 14 s. Calculate the total distance travelled.
v_max = 48 m/s (t₁ = 8 s, t₂ = 14 s) · Distance = Area = ½vt₁ + vt₂
10. On a speed-time graph, a train accelerates uniformly from rest to 50 m/s in 11 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 = 11 s, t₂ = 4 s) · Distance = Area = ½vt₁ + vt₂
11. On a speed-time graph, a train accelerates uniformly from rest to 30 m/s in 6 s and then continues at a constant speed of 30 m/s for a further 5 s. Calculate the total distance travelled.
v_max = 30 m/s (t₁ = 6 s, t₂ = 5 s) · Distance = Area = ½vt₁ + vt₂
12. On a speed-time graph, a train accelerates uniformly from rest to 22 m/s in 5 s and then continues at a constant speed of 22 m/s for a further 5 s. Calculate the total distance travelled.
v_max = 22 m/s (t₁ = 5 s, t₂ = 5 s) · Distance = Area = ½vt₁ + vt₂

12 questions · Seed 104737 · Age guidance, not curriculum certification

View the answer key

Worksheet StudioAnswer key · Ages 16-18

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 4 s and then continues at a constant speed of 18 m/s for a further 15 s. Calculate the total distance travelled.
306 m
Distance is the area under the speed-time graph: triangle area = ½ × 4 × 18 = 36 m, plus rectangle area = 15 × 18 = 270 m. Total distance = 36 + 270 = 306 m.
2. 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 15 s. Calculate the total distance travelled.
144 m
Distance is the area under the speed-time graph: triangle area = ½ × 6 × 8 = 24 m, plus rectangle area = 15 × 8 = 120 m. Total distance = 24 + 120 = 144 m.
3. On a speed-time graph, a train accelerates uniformly from rest to 12 m/s in 8 s and then continues at a constant speed of 12 m/s for a further 14 s. Calculate the total distance travelled.
216 m
Distance is the area under the speed-time graph: triangle area = ½ × 8 × 12 = 48 m, plus rectangle area = 14 × 12 = 168 m. Total distance = 48 + 168 = 216 m.
4. 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 10 s. Calculate the total distance travelled.
120 m
Distance is the area under the speed-time graph: triangle area = ½ × 4 × 10 = 20 m, plus rectangle area = 10 × 10 = 100 m. Total distance = 20 + 100 = 120 m.
5. On a speed-time graph, a train accelerates uniformly from rest to 12 m/s in 8 s and then continues at a constant speed of 12 m/s for a further 5 s. Calculate the total distance travelled.
108 m
Distance is the area under the speed-time graph: triangle area = ½ × 8 × 12 = 48 m, plus rectangle area = 5 × 12 = 60 m. Total distance = 48 + 60 = 108 m.
6. On a speed-time graph, a train accelerates uniformly from rest to 24 m/s in 6 s and then continues at a constant speed of 24 m/s for a further 5 s. Calculate the total distance travelled.
192 m
Distance is the area under the speed-time graph: triangle area = ½ × 6 × 24 = 72 m, plus rectangle area = 5 × 24 = 120 m. Total distance = 72 + 120 = 192 m.
7. On a speed-time graph, a train accelerates uniformly from rest to 28 m/s in 10 s and then continues at a constant speed of 28 m/s for a further 10 s. Calculate the total distance travelled.
420 m
Distance is the area under the speed-time graph: triangle area = ½ × 10 × 28 = 140 m, plus rectangle area = 10 × 28 = 280 m. Total distance = 140 + 280 = 420 m.
8. 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 5 s. Calculate the total distance travelled.
182 m
Distance is the area under the speed-time graph: triangle area = ½ × 3 × 28 = 42 m, plus rectangle area = 5 × 28 = 140 m. Total distance = 42 + 140 = 182 m.
9. 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 14 s. Calculate the total distance travelled.
864 m
Distance is the area under the speed-time graph: triangle area = ½ × 8 × 48 = 192 m, plus rectangle area = 14 × 48 = 672 m. Total distance = 192 + 672 = 864 m.
10. On a speed-time graph, a train accelerates uniformly from rest to 50 m/s in 11 s and then continues at a constant speed of 50 m/s for a further 4 s. Calculate the total distance travelled.
475 m
Distance is the area under the speed-time graph: triangle area = ½ × 11 × 50 = 275 m, plus rectangle area = 4 × 50 = 200 m. Total distance = 275 + 200 = 475 m.
11. On a speed-time graph, a train accelerates uniformly from rest to 30 m/s in 6 s and then continues at a constant speed of 30 m/s for a further 5 s. Calculate the total distance travelled.
240 m
Distance is the area under the speed-time graph: triangle area = ½ × 6 × 30 = 90 m, plus rectangle area = 5 × 30 = 150 m. Total distance = 90 + 150 = 240 m.
12. On a speed-time graph, a train accelerates uniformly from rest to 22 m/s in 5 s and then continues at a constant speed of 22 m/s for a further 5 s. Calculate the total distance travelled.
165 m
Distance is the area under the speed-time graph: triangle area = ½ × 5 × 22 = 55 m, plus rectangle area = 5 × 22 = 110 m. Total distance = 55 + 110 = 165 m.

12 questions · Seed 104737 · Age guidance, not curriculum certification

Worksheet StudioPractice pack · Ages 16-18

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 4 s and then continues at a constant speed of 18 m/s for a further 15 s. Calculate the total distance travelled.
v_max = 18 m/s (t₁ = 4 s, t₂ = 15 s) · Distance = Area = ½vt₁ + vt₂
2. 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 15 s. Calculate the total distance travelled.
v_max = 8 m/s (t₁ = 6 s, t₂ = 15 s) · Distance = Area = ½vt₁ + vt₂
3. On a speed-time graph, a train accelerates uniformly from rest to 12 m/s in 8 s and then continues at a constant speed of 12 m/s for a further 14 s. Calculate the total distance travelled.
v_max = 12 m/s (t₁ = 8 s, t₂ = 14 s) · Distance = Area = ½vt₁ + vt₂
4. 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 10 s. Calculate the total distance travelled.
v_max = 10 m/s (t₁ = 4 s, t₂ = 10 s) · Distance = Area = ½vt₁ + vt₂
5. On a speed-time graph, a train accelerates uniformly from rest to 12 m/s in 8 s and then continues at a constant speed of 12 m/s for a further 5 s. Calculate the total distance travelled.
v_max = 12 m/s (t₁ = 8 s, t₂ = 5 s) · Distance = Area = ½vt₁ + vt₂
6. On a speed-time graph, a train accelerates uniformly from rest to 24 m/s in 6 s and then continues at a constant speed of 24 m/s for a further 5 s. Calculate the total distance travelled.
v_max = 24 m/s (t₁ = 6 s, t₂ = 5 s) · Distance = Area = ½vt₁ + vt₂
7. On a speed-time graph, a train accelerates uniformly from rest to 28 m/s in 10 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 = 10 s, t₂ = 10 s) · Distance = Area = ½vt₁ + vt₂
8. 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 5 s. Calculate the total distance travelled.
v_max = 28 m/s (t₁ = 3 s, t₂ = 5 s) · Distance = Area = ½vt₁ + vt₂
9. 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 14 s. Calculate the total distance travelled.
v_max = 48 m/s (t₁ = 8 s, t₂ = 14 s) · Distance = Area = ½vt₁ + vt₂
10. On a speed-time graph, a train accelerates uniformly from rest to 50 m/s in 11 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 = 11 s, t₂ = 4 s) · Distance = Area = ½vt₁ + vt₂
11. On a speed-time graph, a train accelerates uniformly from rest to 30 m/s in 6 s and then continues at a constant speed of 30 m/s for a further 5 s. Calculate the total distance travelled.
v_max = 30 m/s (t₁ = 6 s, t₂ = 5 s) · Distance = Area = ½vt₁ + vt₂
12. On a speed-time graph, a train accelerates uniformly from rest to 22 m/s in 5 s and then continues at a constant speed of 22 m/s for a further 5 s. Calculate the total distance travelled.
v_max = 22 m/s (t₁ = 5 s, t₂ = 5 s) · Distance = Area = ½vt₁ + vt₂

12 questions · Seed 104737 · Age guidance, not curriculum certification

Worksheet StudioAnswer key · Ages 16-18

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 4 s and then continues at a constant speed of 18 m/s for a further 15 s. Calculate the total distance travelled.
306 m
Distance is the area under the speed-time graph: triangle area = ½ × 4 × 18 = 36 m, plus rectangle area = 15 × 18 = 270 m. Total distance = 36 + 270 = 306 m.
2. 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 15 s. Calculate the total distance travelled.
144 m
Distance is the area under the speed-time graph: triangle area = ½ × 6 × 8 = 24 m, plus rectangle area = 15 × 8 = 120 m. Total distance = 24 + 120 = 144 m.
3. On a speed-time graph, a train accelerates uniformly from rest to 12 m/s in 8 s and then continues at a constant speed of 12 m/s for a further 14 s. Calculate the total distance travelled.
216 m
Distance is the area under the speed-time graph: triangle area = ½ × 8 × 12 = 48 m, plus rectangle area = 14 × 12 = 168 m. Total distance = 48 + 168 = 216 m.
4. 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 10 s. Calculate the total distance travelled.
120 m
Distance is the area under the speed-time graph: triangle area = ½ × 4 × 10 = 20 m, plus rectangle area = 10 × 10 = 100 m. Total distance = 20 + 100 = 120 m.
5. On a speed-time graph, a train accelerates uniformly from rest to 12 m/s in 8 s and then continues at a constant speed of 12 m/s for a further 5 s. Calculate the total distance travelled.
108 m
Distance is the area under the speed-time graph: triangle area = ½ × 8 × 12 = 48 m, plus rectangle area = 5 × 12 = 60 m. Total distance = 48 + 60 = 108 m.
6. On a speed-time graph, a train accelerates uniformly from rest to 24 m/s in 6 s and then continues at a constant speed of 24 m/s for a further 5 s. Calculate the total distance travelled.
192 m
Distance is the area under the speed-time graph: triangle area = ½ × 6 × 24 = 72 m, plus rectangle area = 5 × 24 = 120 m. Total distance = 72 + 120 = 192 m.
7. On a speed-time graph, a train accelerates uniformly from rest to 28 m/s in 10 s and then continues at a constant speed of 28 m/s for a further 10 s. Calculate the total distance travelled.
420 m
Distance is the area under the speed-time graph: triangle area = ½ × 10 × 28 = 140 m, plus rectangle area = 10 × 28 = 280 m. Total distance = 140 + 280 = 420 m.
8. 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 5 s. Calculate the total distance travelled.
182 m
Distance is the area under the speed-time graph: triangle area = ½ × 3 × 28 = 42 m, plus rectangle area = 5 × 28 = 140 m. Total distance = 42 + 140 = 182 m.
9. 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 14 s. Calculate the total distance travelled.
864 m
Distance is the area under the speed-time graph: triangle area = ½ × 8 × 48 = 192 m, plus rectangle area = 14 × 48 = 672 m. Total distance = 192 + 672 = 864 m.
10. On a speed-time graph, a train accelerates uniformly from rest to 50 m/s in 11 s and then continues at a constant speed of 50 m/s for a further 4 s. Calculate the total distance travelled.
475 m
Distance is the area under the speed-time graph: triangle area = ½ × 11 × 50 = 275 m, plus rectangle area = 4 × 50 = 200 m. Total distance = 275 + 200 = 475 m.
11. On a speed-time graph, a train accelerates uniformly from rest to 30 m/s in 6 s and then continues at a constant speed of 30 m/s for a further 5 s. Calculate the total distance travelled.
240 m
Distance is the area under the speed-time graph: triangle area = ½ × 6 × 30 = 90 m, plus rectangle area = 5 × 30 = 150 m. Total distance = 90 + 150 = 240 m.
12. On a speed-time graph, a train accelerates uniformly from rest to 22 m/s in 5 s and then continues at a constant speed of 22 m/s for a further 5 s. Calculate the total distance travelled.
165 m
Distance is the area under the speed-time graph: triangle area = ½ × 5 × 22 = 55 m, plus rectangle area = 5 × 22 = 110 m. Total distance = 55 + 110 = 165 m.

12 questions · Seed 104737 · Age guidance, not curriculum certification