ScienceAges 13-15

Uniform acceleration (s = ut + ½at²)

Use the uniform acceleration equation s = ut + ½at² to calculate displacement from initial velocity, acceleration and time. Review suitability for your learners before teaching.

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Worksheet StudioPractice pack · Ages 13-15

Uniform acceleration (s = ut + ½at²)

Take your time. Show your thinking.

1. A body starts with initial velocity u = 2 m/s and accelerates uniformly at a = 4 m/s² for t = 7 s. Using s = ut + ½at², calculate the distance travelled.
u = 2 m/s, a = 4 m/s² → t = 7 s → s = ? · s = ut + ½at²
2. A body starts with initial velocity u = 13 m/s and accelerates uniformly at a = 8 m/s² for t = 9 s. Using s = ut + ½at², calculate the distance travelled.
u = 13 m/s, a = 8 m/s² → t = 9 s → s = ? · s = ut + ½at²
3. A body starts with initial velocity u = 10 m/s and accelerates uniformly at a = 10 m/s² for t = 9 s. Using s = ut + ½at², calculate the distance travelled.
u = 10 m/s, a = 10 m/s² → t = 9 s → s = ? · s = ut + ½at²
4. A body starts with initial velocity u = 3 m/s and accelerates uniformly at a = 2 m/s² for t = 8 s. Using s = ut + ½at², calculate the distance travelled.
u = 3 m/s, a = 2 m/s² → t = 8 s → s = ? · s = ut + ½at²
5. A body starts with initial velocity u = 13 m/s and accelerates uniformly at a = 4 m/s² for t = 7 s. Using s = ut + ½at², calculate the distance travelled.
u = 13 m/s, a = 4 m/s² → t = 7 s → s = ? · s = ut + ½at²
6. A body starts with initial velocity u = 19 m/s and accelerates uniformly at a = 16 m/s² for t = 8 s. Using s = ut + ½at², calculate the distance travelled.
u = 19 m/s, a = 16 m/s² → t = 8 s → s = ? · s = ut + ½at²
7. A body starts with initial velocity u = 15 m/s and accelerates uniformly at a = 4 m/s² for t = 6 s. Using s = ut + ½at², calculate the distance travelled.
u = 15 m/s, a = 4 m/s² → t = 6 s → s = ? · s = ut + ½at²
8. A body starts with initial velocity u = 20 m/s and accelerates uniformly at a = 12 m/s² for t = 2 s. Using s = ut + ½at², calculate the distance travelled.
u = 20 m/s, a = 12 m/s² → t = 2 s → s = ? · s = ut + ½at²
9. A body starts with initial velocity u = 4 m/s and accelerates uniformly at a = 16 m/s² for t = 3 s. Using s = ut + ½at², calculate the distance travelled.
u = 4 m/s, a = 16 m/s² → t = 3 s → s = ? · s = ut + ½at²
10. A body starts with initial velocity u = 2 m/s and accelerates uniformly at a = 10 m/s² for t = 2 s. Using s = ut + ½at², calculate the distance travelled.
u = 2 m/s, a = 10 m/s² → t = 2 s → s = ? · s = ut + ½at²
11. A body starts with initial velocity u = 3 m/s and accelerates uniformly at a = 14 m/s² for t = 9 s. Using s = ut + ½at², calculate the distance travelled.
u = 3 m/s, a = 14 m/s² → t = 9 s → s = ? · s = ut + ½at²
12. A body starts with initial velocity u = 12 m/s and accelerates uniformly at a = 8 m/s² for t = 3 s. Using s = ut + ½at², calculate the distance travelled.
u = 12 m/s, a = 8 m/s² → t = 3 s → s = ? · s = ut + ½at²

12 questions · Seed 104729 · Age guidance, not curriculum certification

View the answer key

Worksheet StudioAnswer key · Ages 13-15

Uniform acceleration (s = ut + ½at²)

Answers and reasoning. Review before teaching.

1. A body starts with initial velocity u = 2 m/s and accelerates uniformly at a = 4 m/s² for t = 7 s. Using s = ut + ½at², calculate the distance travelled.
112 m
s = (2 × 7) + (½ × 4 × 7²) = 14 + 98 = 112 m.
2. A body starts with initial velocity u = 13 m/s and accelerates uniformly at a = 8 m/s² for t = 9 s. Using s = ut + ½at², calculate the distance travelled.
441 m
s = (13 × 9) + (½ × 8 × 9²) = 117 + 324 = 441 m.
3. A body starts with initial velocity u = 10 m/s and accelerates uniformly at a = 10 m/s² for t = 9 s. Using s = ut + ½at², calculate the distance travelled.
495 m
s = (10 × 9) + (½ × 10 × 9²) = 90 + 405 = 495 m.
4. A body starts with initial velocity u = 3 m/s and accelerates uniformly at a = 2 m/s² for t = 8 s. Using s = ut + ½at², calculate the distance travelled.
88 m
s = (3 × 8) + (½ × 2 × 8²) = 24 + 64 = 88 m.
5. A body starts with initial velocity u = 13 m/s and accelerates uniformly at a = 4 m/s² for t = 7 s. Using s = ut + ½at², calculate the distance travelled.
189 m
s = (13 × 7) + (½ × 4 × 7²) = 91 + 98 = 189 m.
6. A body starts with initial velocity u = 19 m/s and accelerates uniformly at a = 16 m/s² for t = 8 s. Using s = ut + ½at², calculate the distance travelled.
664 m
s = (19 × 8) + (½ × 16 × 8²) = 152 + 512 = 664 m.
7. A body starts with initial velocity u = 15 m/s and accelerates uniformly at a = 4 m/s² for t = 6 s. Using s = ut + ½at², calculate the distance travelled.
162 m
s = (15 × 6) + (½ × 4 × 6²) = 90 + 72 = 162 m.
8. A body starts with initial velocity u = 20 m/s and accelerates uniformly at a = 12 m/s² for t = 2 s. Using s = ut + ½at², calculate the distance travelled.
64 m
s = (20 × 2) + (½ × 12 × 2²) = 40 + 24 = 64 m.
9. A body starts with initial velocity u = 4 m/s and accelerates uniformly at a = 16 m/s² for t = 3 s. Using s = ut + ½at², calculate the distance travelled.
84 m
s = (4 × 3) + (½ × 16 × 3²) = 12 + 72 = 84 m.
10. A body starts with initial velocity u = 2 m/s and accelerates uniformly at a = 10 m/s² for t = 2 s. Using s = ut + ½at², calculate the distance travelled.
24 m
s = (2 × 2) + (½ × 10 × 2²) = 4 + 20 = 24 m.
11. A body starts with initial velocity u = 3 m/s and accelerates uniformly at a = 14 m/s² for t = 9 s. Using s = ut + ½at², calculate the distance travelled.
594 m
s = (3 × 9) + (½ × 14 × 9²) = 27 + 567 = 594 m.
12. A body starts with initial velocity u = 12 m/s and accelerates uniformly at a = 8 m/s² for t = 3 s. Using s = ut + ½at², calculate the distance travelled.
72 m
s = (12 × 3) + (½ × 8 × 3²) = 36 + 36 = 72 m.

12 questions · Seed 104729 · Age guidance, not curriculum certification

Worksheet StudioPractice pack · Ages 13-15

Uniform acceleration (s = ut + ½at²)

Take your time. Show your thinking.

1. A body starts with initial velocity u = 2 m/s and accelerates uniformly at a = 4 m/s² for t = 7 s. Using s = ut + ½at², calculate the distance travelled.
u = 2 m/s, a = 4 m/s² → t = 7 s → s = ? · s = ut + ½at²
2. A body starts with initial velocity u = 13 m/s and accelerates uniformly at a = 8 m/s² for t = 9 s. Using s = ut + ½at², calculate the distance travelled.
u = 13 m/s, a = 8 m/s² → t = 9 s → s = ? · s = ut + ½at²
3. A body starts with initial velocity u = 10 m/s and accelerates uniformly at a = 10 m/s² for t = 9 s. Using s = ut + ½at², calculate the distance travelled.
u = 10 m/s, a = 10 m/s² → t = 9 s → s = ? · s = ut + ½at²
4. A body starts with initial velocity u = 3 m/s and accelerates uniformly at a = 2 m/s² for t = 8 s. Using s = ut + ½at², calculate the distance travelled.
u = 3 m/s, a = 2 m/s² → t = 8 s → s = ? · s = ut + ½at²
5. A body starts with initial velocity u = 13 m/s and accelerates uniformly at a = 4 m/s² for t = 7 s. Using s = ut + ½at², calculate the distance travelled.
u = 13 m/s, a = 4 m/s² → t = 7 s → s = ? · s = ut + ½at²
6. A body starts with initial velocity u = 19 m/s and accelerates uniformly at a = 16 m/s² for t = 8 s. Using s = ut + ½at², calculate the distance travelled.
u = 19 m/s, a = 16 m/s² → t = 8 s → s = ? · s = ut + ½at²
7. A body starts with initial velocity u = 15 m/s and accelerates uniformly at a = 4 m/s² for t = 6 s. Using s = ut + ½at², calculate the distance travelled.
u = 15 m/s, a = 4 m/s² → t = 6 s → s = ? · s = ut + ½at²
8. A body starts with initial velocity u = 20 m/s and accelerates uniformly at a = 12 m/s² for t = 2 s. Using s = ut + ½at², calculate the distance travelled.
u = 20 m/s, a = 12 m/s² → t = 2 s → s = ? · s = ut + ½at²
9. A body starts with initial velocity u = 4 m/s and accelerates uniformly at a = 16 m/s² for t = 3 s. Using s = ut + ½at², calculate the distance travelled.
u = 4 m/s, a = 16 m/s² → t = 3 s → s = ? · s = ut + ½at²
10. A body starts with initial velocity u = 2 m/s and accelerates uniformly at a = 10 m/s² for t = 2 s. Using s = ut + ½at², calculate the distance travelled.
u = 2 m/s, a = 10 m/s² → t = 2 s → s = ? · s = ut + ½at²
11. A body starts with initial velocity u = 3 m/s and accelerates uniformly at a = 14 m/s² for t = 9 s. Using s = ut + ½at², calculate the distance travelled.
u = 3 m/s, a = 14 m/s² → t = 9 s → s = ? · s = ut + ½at²
12. A body starts with initial velocity u = 12 m/s and accelerates uniformly at a = 8 m/s² for t = 3 s. Using s = ut + ½at², calculate the distance travelled.
u = 12 m/s, a = 8 m/s² → t = 3 s → s = ? · s = ut + ½at²

12 questions · Seed 104729 · Age guidance, not curriculum certification

Worksheet StudioAnswer key · Ages 13-15

Uniform acceleration (s = ut + ½at²)

Answers and reasoning. Review before teaching.

1. A body starts with initial velocity u = 2 m/s and accelerates uniformly at a = 4 m/s² for t = 7 s. Using s = ut + ½at², calculate the distance travelled.
112 m
s = (2 × 7) + (½ × 4 × 7²) = 14 + 98 = 112 m.
2. A body starts with initial velocity u = 13 m/s and accelerates uniformly at a = 8 m/s² for t = 9 s. Using s = ut + ½at², calculate the distance travelled.
441 m
s = (13 × 9) + (½ × 8 × 9²) = 117 + 324 = 441 m.
3. A body starts with initial velocity u = 10 m/s and accelerates uniformly at a = 10 m/s² for t = 9 s. Using s = ut + ½at², calculate the distance travelled.
495 m
s = (10 × 9) + (½ × 10 × 9²) = 90 + 405 = 495 m.
4. A body starts with initial velocity u = 3 m/s and accelerates uniformly at a = 2 m/s² for t = 8 s. Using s = ut + ½at², calculate the distance travelled.
88 m
s = (3 × 8) + (½ × 2 × 8²) = 24 + 64 = 88 m.
5. A body starts with initial velocity u = 13 m/s and accelerates uniformly at a = 4 m/s² for t = 7 s. Using s = ut + ½at², calculate the distance travelled.
189 m
s = (13 × 7) + (½ × 4 × 7²) = 91 + 98 = 189 m.
6. A body starts with initial velocity u = 19 m/s and accelerates uniformly at a = 16 m/s² for t = 8 s. Using s = ut + ½at², calculate the distance travelled.
664 m
s = (19 × 8) + (½ × 16 × 8²) = 152 + 512 = 664 m.
7. A body starts with initial velocity u = 15 m/s and accelerates uniformly at a = 4 m/s² for t = 6 s. Using s = ut + ½at², calculate the distance travelled.
162 m
s = (15 × 6) + (½ × 4 × 6²) = 90 + 72 = 162 m.
8. A body starts with initial velocity u = 20 m/s and accelerates uniformly at a = 12 m/s² for t = 2 s. Using s = ut + ½at², calculate the distance travelled.
64 m
s = (20 × 2) + (½ × 12 × 2²) = 40 + 24 = 64 m.
9. A body starts with initial velocity u = 4 m/s and accelerates uniformly at a = 16 m/s² for t = 3 s. Using s = ut + ½at², calculate the distance travelled.
84 m
s = (4 × 3) + (½ × 16 × 3²) = 12 + 72 = 84 m.
10. A body starts with initial velocity u = 2 m/s and accelerates uniformly at a = 10 m/s² for t = 2 s. Using s = ut + ½at², calculate the distance travelled.
24 m
s = (2 × 2) + (½ × 10 × 2²) = 4 + 20 = 24 m.
11. A body starts with initial velocity u = 3 m/s and accelerates uniformly at a = 14 m/s² for t = 9 s. Using s = ut + ½at², calculate the distance travelled.
594 m
s = (3 × 9) + (½ × 14 × 9²) = 27 + 567 = 594 m.
12. A body starts with initial velocity u = 12 m/s and accelerates uniformly at a = 8 m/s² for t = 3 s. Using s = ut + ½at², calculate the distance travelled.
72 m
s = (12 × 3) + (½ × 8 × 3²) = 36 + 36 = 72 m.

12 questions · Seed 104729 · Age guidance, not curriculum certification