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 = 9 m/s and accelerates uniformly at a = 12 m/s² for t = 5 s. Using s = ut + ½at², calculate the distance travelled.
u = 9 m/s, a = 12 m/s² → t = 5 s → s = ? · s = ut + ½at²
2. A body starts with initial velocity u = 7 m/s and accelerates uniformly at a = 10 m/s² for t = 6 s. Using s = ut + ½at², calculate the distance travelled.
u = 7 m/s, a = 10 m/s² → t = 6 s → s = ? · s = ut + ½at²
3. A body starts with initial velocity u = 14 m/s and accelerates uniformly at a = 2 m/s² for t = 8 s. Using s = ut + ½at², calculate the distance travelled.
u = 14 m/s, a = 2 m/s² → t = 8 s → s = ? · s = ut + ½at²
4. A body starts with initial velocity u = 4 m/s and accelerates uniformly at a = 2 m/s² for t = 7 s. Using s = ut + ½at², calculate the distance travelled.
u = 4 m/s, a = 2 m/s² → t = 7 s → s = ? · s = ut + ½at²
5. A body starts with initial velocity u = 18 m/s and accelerates uniformly at a = 12 m/s² for t = 7 s. Using s = ut + ½at², calculate the distance travelled.
u = 18 m/s, a = 12 m/s² → t = 7 s → s = ? · s = ut + ½at²
6. A body starts with initial velocity u = 14 m/s and accelerates uniformly at a = 8 m/s² for t = 2 s. Using s = ut + ½at², calculate the distance travelled.
u = 14 m/s, a = 8 m/s² → t = 2 s → s = ? · s = ut + ½at²
7. A body starts with initial velocity u = 2 m/s and accelerates uniformly at a = 6 m/s² for t = 2 s. Using s = ut + ½at², calculate the distance travelled.
u = 2 m/s, a = 6 m/s² → t = 2 s → s = ? · s = ut + ½at²
8. A body starts with initial velocity u = 16 m/s and accelerates uniformly at a = 6 m/s² for t = 9 s. Using s = ut + ½at², calculate the distance travelled.
u = 16 m/s, a = 6 m/s² → t = 9 s → s = ? · s = ut + ½at²
9. A body starts with initial velocity u = 19 m/s and accelerates uniformly at a = 8 m/s² for t = 6 s. Using s = ut + ½at², calculate the distance travelled.
u = 19 m/s, a = 8 m/s² → t = 6 s → s = ? · s = ut + ½at²
10. A body starts with initial velocity u = 9 m/s and accelerates uniformly at a = 16 m/s² for t = 5 s. Using s = ut + ½at², calculate the distance travelled.
u = 9 m/s, a = 16 m/s² → t = 5 s → s = ? · s = ut + ½at²
11. A body starts with initial velocity u = 19 m/s and accelerates uniformly at a = 12 m/s² for t = 4 s. Using s = ut + ½at², calculate the distance travelled.
u = 19 m/s, a = 12 m/s² → t = 4 s → s = ? · s = ut + ½at²
12. A body starts with initial velocity u = 15 m/s and accelerates uniformly at a = 6 m/s² for t = 4 s. Using s = ut + ½at², calculate the distance travelled.
u = 15 m/s, a = 6 m/s² → t = 4 s → s = ? · s = ut + ½at²

12 questions · Seed 42 · 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 = 9 m/s and accelerates uniformly at a = 12 m/s² for t = 5 s. Using s = ut + ½at², calculate the distance travelled.
195 m
s = (9 × 5) + (½ × 12 × 5²) = 45 + 150 = 195 m.
2. A body starts with initial velocity u = 7 m/s and accelerates uniformly at a = 10 m/s² for t = 6 s. Using s = ut + ½at², calculate the distance travelled.
222 m
s = (7 × 6) + (½ × 10 × 6²) = 42 + 180 = 222 m.
3. A body starts with initial velocity u = 14 m/s and accelerates uniformly at a = 2 m/s² for t = 8 s. Using s = ut + ½at², calculate the distance travelled.
176 m
s = (14 × 8) + (½ × 2 × 8²) = 112 + 64 = 176 m.
4. A body starts with initial velocity u = 4 m/s and accelerates uniformly at a = 2 m/s² for t = 7 s. Using s = ut + ½at², calculate the distance travelled.
77 m
s = (4 × 7) + (½ × 2 × 7²) = 28 + 49 = 77 m.
5. A body starts with initial velocity u = 18 m/s and accelerates uniformly at a = 12 m/s² for t = 7 s. Using s = ut + ½at², calculate the distance travelled.
420 m
s = (18 × 7) + (½ × 12 × 7²) = 126 + 294 = 420 m.
6. A body starts with initial velocity u = 14 m/s and accelerates uniformly at a = 8 m/s² for t = 2 s. Using s = ut + ½at², calculate the distance travelled.
44 m
s = (14 × 2) + (½ × 8 × 2²) = 28 + 16 = 44 m.
7. A body starts with initial velocity u = 2 m/s and accelerates uniformly at a = 6 m/s² for t = 2 s. Using s = ut + ½at², calculate the distance travelled.
16 m
s = (2 × 2) + (½ × 6 × 2²) = 4 + 12 = 16 m.
8. A body starts with initial velocity u = 16 m/s and accelerates uniformly at a = 6 m/s² for t = 9 s. Using s = ut + ½at², calculate the distance travelled.
387 m
s = (16 × 9) + (½ × 6 × 9²) = 144 + 243 = 387 m.
9. A body starts with initial velocity u = 19 m/s and accelerates uniformly at a = 8 m/s² for t = 6 s. Using s = ut + ½at², calculate the distance travelled.
258 m
s = (19 × 6) + (½ × 8 × 6²) = 114 + 144 = 258 m.
10. A body starts with initial velocity u = 9 m/s and accelerates uniformly at a = 16 m/s² for t = 5 s. Using s = ut + ½at², calculate the distance travelled.
245 m
s = (9 × 5) + (½ × 16 × 5²) = 45 + 200 = 245 m.
11. A body starts with initial velocity u = 19 m/s and accelerates uniformly at a = 12 m/s² for t = 4 s. Using s = ut + ½at², calculate the distance travelled.
172 m
s = (19 × 4) + (½ × 12 × 4²) = 76 + 96 = 172 m.
12. A body starts with initial velocity u = 15 m/s and accelerates uniformly at a = 6 m/s² for t = 4 s. Using s = ut + ½at², calculate the distance travelled.
108 m
s = (15 × 4) + (½ × 6 × 4²) = 60 + 48 = 108 m.

12 questions · Seed 42 · 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 = 9 m/s and accelerates uniformly at a = 12 m/s² for t = 5 s. Using s = ut + ½at², calculate the distance travelled.
u = 9 m/s, a = 12 m/s² → t = 5 s → s = ? · s = ut + ½at²
2. A body starts with initial velocity u = 7 m/s and accelerates uniformly at a = 10 m/s² for t = 6 s. Using s = ut + ½at², calculate the distance travelled.
u = 7 m/s, a = 10 m/s² → t = 6 s → s = ? · s = ut + ½at²
3. A body starts with initial velocity u = 14 m/s and accelerates uniformly at a = 2 m/s² for t = 8 s. Using s = ut + ½at², calculate the distance travelled.
u = 14 m/s, a = 2 m/s² → t = 8 s → s = ? · s = ut + ½at²
4. A body starts with initial velocity u = 4 m/s and accelerates uniformly at a = 2 m/s² for t = 7 s. Using s = ut + ½at², calculate the distance travelled.
u = 4 m/s, a = 2 m/s² → t = 7 s → s = ? · s = ut + ½at²
5. A body starts with initial velocity u = 18 m/s and accelerates uniformly at a = 12 m/s² for t = 7 s. Using s = ut + ½at², calculate the distance travelled.
u = 18 m/s, a = 12 m/s² → t = 7 s → s = ? · s = ut + ½at²
6. A body starts with initial velocity u = 14 m/s and accelerates uniformly at a = 8 m/s² for t = 2 s. Using s = ut + ½at², calculate the distance travelled.
u = 14 m/s, a = 8 m/s² → t = 2 s → s = ? · s = ut + ½at²
7. A body starts with initial velocity u = 2 m/s and accelerates uniformly at a = 6 m/s² for t = 2 s. Using s = ut + ½at², calculate the distance travelled.
u = 2 m/s, a = 6 m/s² → t = 2 s → s = ? · s = ut + ½at²
8. A body starts with initial velocity u = 16 m/s and accelerates uniformly at a = 6 m/s² for t = 9 s. Using s = ut + ½at², calculate the distance travelled.
u = 16 m/s, a = 6 m/s² → t = 9 s → s = ? · s = ut + ½at²
9. A body starts with initial velocity u = 19 m/s and accelerates uniformly at a = 8 m/s² for t = 6 s. Using s = ut + ½at², calculate the distance travelled.
u = 19 m/s, a = 8 m/s² → t = 6 s → s = ? · s = ut + ½at²
10. A body starts with initial velocity u = 9 m/s and accelerates uniformly at a = 16 m/s² for t = 5 s. Using s = ut + ½at², calculate the distance travelled.
u = 9 m/s, a = 16 m/s² → t = 5 s → s = ? · s = ut + ½at²
11. A body starts with initial velocity u = 19 m/s and accelerates uniformly at a = 12 m/s² for t = 4 s. Using s = ut + ½at², calculate the distance travelled.
u = 19 m/s, a = 12 m/s² → t = 4 s → s = ? · s = ut + ½at²
12. A body starts with initial velocity u = 15 m/s and accelerates uniformly at a = 6 m/s² for t = 4 s. Using s = ut + ½at², calculate the distance travelled.
u = 15 m/s, a = 6 m/s² → t = 4 s → s = ? · s = ut + ½at²

12 questions · Seed 42 · 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 = 9 m/s and accelerates uniformly at a = 12 m/s² for t = 5 s. Using s = ut + ½at², calculate the distance travelled.
195 m
s = (9 × 5) + (½ × 12 × 5²) = 45 + 150 = 195 m.
2. A body starts with initial velocity u = 7 m/s and accelerates uniformly at a = 10 m/s² for t = 6 s. Using s = ut + ½at², calculate the distance travelled.
222 m
s = (7 × 6) + (½ × 10 × 6²) = 42 + 180 = 222 m.
3. A body starts with initial velocity u = 14 m/s and accelerates uniformly at a = 2 m/s² for t = 8 s. Using s = ut + ½at², calculate the distance travelled.
176 m
s = (14 × 8) + (½ × 2 × 8²) = 112 + 64 = 176 m.
4. A body starts with initial velocity u = 4 m/s and accelerates uniformly at a = 2 m/s² for t = 7 s. Using s = ut + ½at², calculate the distance travelled.
77 m
s = (4 × 7) + (½ × 2 × 7²) = 28 + 49 = 77 m.
5. A body starts with initial velocity u = 18 m/s and accelerates uniformly at a = 12 m/s² for t = 7 s. Using s = ut + ½at², calculate the distance travelled.
420 m
s = (18 × 7) + (½ × 12 × 7²) = 126 + 294 = 420 m.
6. A body starts with initial velocity u = 14 m/s and accelerates uniformly at a = 8 m/s² for t = 2 s. Using s = ut + ½at², calculate the distance travelled.
44 m
s = (14 × 2) + (½ × 8 × 2²) = 28 + 16 = 44 m.
7. A body starts with initial velocity u = 2 m/s and accelerates uniformly at a = 6 m/s² for t = 2 s. Using s = ut + ½at², calculate the distance travelled.
16 m
s = (2 × 2) + (½ × 6 × 2²) = 4 + 12 = 16 m.
8. A body starts with initial velocity u = 16 m/s and accelerates uniformly at a = 6 m/s² for t = 9 s. Using s = ut + ½at², calculate the distance travelled.
387 m
s = (16 × 9) + (½ × 6 × 9²) = 144 + 243 = 387 m.
9. A body starts with initial velocity u = 19 m/s and accelerates uniformly at a = 8 m/s² for t = 6 s. Using s = ut + ½at², calculate the distance travelled.
258 m
s = (19 × 6) + (½ × 8 × 6²) = 114 + 144 = 258 m.
10. A body starts with initial velocity u = 9 m/s and accelerates uniformly at a = 16 m/s² for t = 5 s. Using s = ut + ½at², calculate the distance travelled.
245 m
s = (9 × 5) + (½ × 16 × 5²) = 45 + 200 = 245 m.
11. A body starts with initial velocity u = 19 m/s and accelerates uniformly at a = 12 m/s² for t = 4 s. Using s = ut + ½at², calculate the distance travelled.
172 m
s = (19 × 4) + (½ × 12 × 4²) = 76 + 96 = 172 m.
12. A body starts with initial velocity u = 15 m/s and accelerates uniformly at a = 6 m/s² for t = 4 s. Using s = ut + ½at², calculate the distance travelled.
108 m
s = (15 × 4) + (½ × 6 × 4²) = 60 + 48 = 108 m.

12 questions · Seed 42 · Age guidance, not curriculum certification