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

12 questions · Seed 45 · 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 = 7 m/s and accelerates uniformly at a = 2 m/s² for t = 6 s. Using s = ut + ½at², calculate the distance travelled.
78 m
s = (7 × 6) + (½ × 2 × 6²) = 42 + 36 = 78 m.
2. A body starts with initial velocity u = 15 m/s and accelerates uniformly at a = 16 m/s² for t = 4 s. Using s = ut + ½at², calculate the distance travelled.
188 m
s = (15 × 4) + (½ × 16 × 4²) = 60 + 128 = 188 m.
3. A body starts with initial velocity u = 15 m/s and accelerates uniformly at a = 14 m/s² for t = 4 s. Using s = ut + ½at², calculate the distance travelled.
172 m
s = (15 × 4) + (½ × 14 × 4²) = 60 + 112 = 172 m.
4. A body starts with initial velocity u = 5 m/s and accelerates uniformly at a = 2 m/s² for t = 2 s. Using s = ut + ½at², calculate the distance travelled.
14 m
s = (5 × 2) + (½ × 2 × 2²) = 10 + 4 = 14 m.
5. A body starts with initial velocity u = 19 m/s and accelerates uniformly at a = 12 m/s² for t = 2 s. Using s = ut + ½at², calculate the distance travelled.
62 m
s = (19 × 2) + (½ × 12 × 2²) = 38 + 24 = 62 m.
6. A body starts with initial velocity u = 9 m/s and accelerates uniformly at a = 2 m/s² for t = 3 s. Using s = ut + ½at², calculate the distance travelled.
36 m
s = (9 × 3) + (½ × 2 × 3²) = 27 + 9 = 36 m.
7. 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.
8. A body starts with initial velocity u = 14 m/s and accelerates uniformly at a = 2 m/s² for t = 4 s. Using s = ut + ½at², calculate the distance travelled.
72 m
s = (14 × 4) + (½ × 2 × 4²) = 56 + 16 = 72 m.
9. A body starts with initial velocity u = 13 m/s and accelerates uniformly at a = 10 m/s² for t = 5 s. Using s = ut + ½at², calculate the distance travelled.
190 m
s = (13 × 5) + (½ × 10 × 5²) = 65 + 125 = 190 m.
10. A body starts with initial velocity u = 19 m/s and accelerates uniformly at a = 14 m/s² for t = 3 s. Using s = ut + ½at², calculate the distance travelled.
120 m
s = (19 × 3) + (½ × 14 × 3²) = 57 + 63 = 120 m.
11. A body starts with initial velocity u = 3 m/s and accelerates uniformly at a = 16 m/s² for t = 5 s. Using s = ut + ½at², calculate the distance travelled.
215 m
s = (3 × 5) + (½ × 16 × 5²) = 15 + 200 = 215 m.
12. A body starts with initial velocity u = 20 m/s and accelerates uniformly at a = 8 m/s² for t = 8 s. Using s = ut + ½at², calculate the distance travelled.
416 m
s = (20 × 8) + (½ × 8 × 8²) = 160 + 256 = 416 m.

12 questions · Seed 45 · 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 = 7 m/s and accelerates uniformly at a = 2 m/s² for t = 6 s. Using s = ut + ½at², calculate the distance travelled.
u = 7 m/s, a = 2 m/s² → t = 6 s → s = ? · s = ut + ½at²
2. A body starts with initial velocity u = 15 m/s and accelerates uniformly at a = 16 m/s² for t = 4 s. Using s = ut + ½at², calculate the distance travelled.
u = 15 m/s, a = 16 m/s² → t = 4 s → s = ? · s = ut + ½at²
3. A body starts with initial velocity u = 15 m/s and accelerates uniformly at a = 14 m/s² for t = 4 s. Using s = ut + ½at², calculate the distance travelled.
u = 15 m/s, a = 14 m/s² → t = 4 s → s = ? · s = ut + ½at²
4. A body starts with initial velocity u = 5 m/s and accelerates uniformly at a = 2 m/s² for t = 2 s. Using s = ut + ½at², calculate the distance travelled.
u = 5 m/s, a = 2 m/s² → t = 2 s → s = ? · s = ut + ½at²
5. A body starts with initial velocity u = 19 m/s and accelerates uniformly at a = 12 m/s² for t = 2 s. Using s = ut + ½at², calculate the distance travelled.
u = 19 m/s, a = 12 m/s² → t = 2 s → s = ? · s = ut + ½at²
6. A body starts with initial velocity u = 9 m/s and accelerates uniformly at a = 2 m/s² for t = 3 s. Using s = ut + ½at², calculate the distance travelled.
u = 9 m/s, a = 2 m/s² → t = 3 s → s = ? · s = ut + ½at²
7. 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
8. A body starts with initial velocity u = 14 m/s and accelerates uniformly at a = 2 m/s² for t = 4 s. Using s = ut + ½at², calculate the distance travelled.
u = 14 m/s, a = 2 m/s² → t = 4 s → s = ? · s = ut + ½at²
9. A body starts with initial velocity u = 13 m/s and accelerates uniformly at a = 10 m/s² for t = 5 s. Using s = ut + ½at², calculate the distance travelled.
u = 13 m/s, a = 10 m/s² → t = 5 s → s = ? · s = ut + ½at²
10. A body starts with initial velocity u = 19 m/s and accelerates uniformly at a = 14 m/s² for t = 3 s. Using s = ut + ½at², calculate the distance travelled.
u = 19 m/s, a = 14 m/s² → t = 3 s → s = ? · s = ut + ½at²
11. A body starts with initial velocity u = 3 m/s and accelerates uniformly at a = 16 m/s² for t = 5 s. Using s = ut + ½at², calculate the distance travelled.
u = 3 m/s, a = 16 m/s² → t = 5 s → s = ? · s = ut + ½at²
12. A body starts with initial velocity u = 20 m/s and accelerates uniformly at a = 8 m/s² for t = 8 s. Using s = ut + ½at², calculate the distance travelled.
u = 20 m/s, a = 8 m/s² → t = 8 s → s = ? · s = ut + ½at²

12 questions · Seed 45 · 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 = 7 m/s and accelerates uniformly at a = 2 m/s² for t = 6 s. Using s = ut + ½at², calculate the distance travelled.
78 m
s = (7 × 6) + (½ × 2 × 6²) = 42 + 36 = 78 m.
2. A body starts with initial velocity u = 15 m/s and accelerates uniformly at a = 16 m/s² for t = 4 s. Using s = ut + ½at², calculate the distance travelled.
188 m
s = (15 × 4) + (½ × 16 × 4²) = 60 + 128 = 188 m.
3. A body starts with initial velocity u = 15 m/s and accelerates uniformly at a = 14 m/s² for t = 4 s. Using s = ut + ½at², calculate the distance travelled.
172 m
s = (15 × 4) + (½ × 14 × 4²) = 60 + 112 = 172 m.
4. A body starts with initial velocity u = 5 m/s and accelerates uniformly at a = 2 m/s² for t = 2 s. Using s = ut + ½at², calculate the distance travelled.
14 m
s = (5 × 2) + (½ × 2 × 2²) = 10 + 4 = 14 m.
5. A body starts with initial velocity u = 19 m/s and accelerates uniformly at a = 12 m/s² for t = 2 s. Using s = ut + ½at², calculate the distance travelled.
62 m
s = (19 × 2) + (½ × 12 × 2²) = 38 + 24 = 62 m.
6. A body starts with initial velocity u = 9 m/s and accelerates uniformly at a = 2 m/s² for t = 3 s. Using s = ut + ½at², calculate the distance travelled.
36 m
s = (9 × 3) + (½ × 2 × 3²) = 27 + 9 = 36 m.
7. 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.
8. A body starts with initial velocity u = 14 m/s and accelerates uniformly at a = 2 m/s² for t = 4 s. Using s = ut + ½at², calculate the distance travelled.
72 m
s = (14 × 4) + (½ × 2 × 4²) = 56 + 16 = 72 m.
9. A body starts with initial velocity u = 13 m/s and accelerates uniformly at a = 10 m/s² for t = 5 s. Using s = ut + ½at², calculate the distance travelled.
190 m
s = (13 × 5) + (½ × 10 × 5²) = 65 + 125 = 190 m.
10. A body starts with initial velocity u = 19 m/s and accelerates uniformly at a = 14 m/s² for t = 3 s. Using s = ut + ½at², calculate the distance travelled.
120 m
s = (19 × 3) + (½ × 14 × 3²) = 57 + 63 = 120 m.
11. A body starts with initial velocity u = 3 m/s and accelerates uniformly at a = 16 m/s² for t = 5 s. Using s = ut + ½at², calculate the distance travelled.
215 m
s = (3 × 5) + (½ × 16 × 5²) = 15 + 200 = 215 m.
12. A body starts with initial velocity u = 20 m/s and accelerates uniformly at a = 8 m/s² for t = 8 s. Using s = ut + ½at², calculate the distance travelled.
416 m
s = (20 × 8) + (½ × 8 × 8²) = 160 + 256 = 416 m.

12 questions · Seed 45 · Age guidance, not curriculum certification