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 = 20 m/s and accelerates uniformly at a = 4 m/s² for t = 5 s. Using s = ut + ½at², calculate the distance travelled.
u = 20 m/s, a = 4 m/s² → t = 5 s → s = ? · s = ut + ½at²
2. A body starts with initial velocity u = 2 m/s and accelerates uniformly at a = 14 m/s² for t = 8 s. Using s = ut + ½at², calculate the distance travelled.
u = 2 m/s, a = 14 m/s² → t = 8 s → s = ? · s = ut + ½at²
3. A body starts with initial velocity u = 7 m/s and accelerates uniformly at a = 10 m/s² for t = 8 s. Using s = ut + ½at², calculate the distance travelled.
u = 7 m/s, a = 10 m/s² → t = 8 s → s = ? · s = ut + ½at²
4. A body starts with initial velocity u = 8 m/s and accelerates uniformly at a = 4 m/s² for t = 3 s. Using s = ut + ½at², calculate the distance travelled.
u = 8 m/s, a = 4 m/s² → t = 3 s → s = ? · s = ut + ½at²
5. A body starts with initial velocity u = 19 m/s and accelerates uniformly at a = 10 m/s² for t = 5 s. Using s = ut + ½at², calculate the distance travelled.
u = 19 m/s, a = 10 m/s² → t = 5 s → s = ? · s = ut + ½at²
6. A body starts with initial velocity u = 8 m/s and accelerates uniformly at a = 16 m/s² for t = 9 s. Using s = ut + ½at², calculate the distance travelled.
u = 8 m/s, a = 16 m/s² → t = 9 s → s = ? · s = ut + ½at²
7. A body starts with initial velocity u = 13 m/s and accelerates uniformly at a = 14 m/s² for t = 2 s. Using s = ut + ½at², calculate the distance travelled.
u = 13 m/s, a = 14 m/s² → t = 2 s → s = ? · s = ut + ½at²
8. A body starts with initial velocity u = 7 m/s and accelerates uniformly at a = 4 m/s² for t = 8 s. Using s = ut + ½at², calculate the distance travelled.
u = 7 m/s, a = 4 m/s² → t = 8 s → s = ? · s = ut + ½at²
9. A body starts with initial velocity u = 17 m/s and accelerates uniformly at a = 2 m/s² for t = 6 s. Using s = ut + ½at², calculate the distance travelled.
u = 17 m/s, a = 2 m/s² → t = 6 s → s = ? · s = ut + ½at²
10. A body starts with initial velocity u = 12 m/s and accelerates uniformly at a = 2 m/s² for t = 3 s. Using s = ut + ½at², calculate the distance travelled.
u = 12 m/s, a = 2 m/s² → t = 3 s → s = ? · s = ut + ½at²
11. A body starts with initial velocity u = 14 m/s and accelerates uniformly at a = 14 m/s² for t = 3 s. Using s = ut + ½at², calculate the distance travelled.
u = 14 m/s, a = 14 m/s² → t = 3 s → s = ? · s = ut + ½at²
12. A body starts with initial velocity u = 4 m/s and accelerates uniformly at a = 10 m/s² for t = 2 s. Using s = ut + ½at², calculate the distance travelled.
u = 4 m/s, a = 10 m/s² → t = 2 s → s = ? · s = ut + ½at²

12 questions · Seed 43 · 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 = 20 m/s and accelerates uniformly at a = 4 m/s² for t = 5 s. Using s = ut + ½at², calculate the distance travelled.
150 m
s = (20 × 5) + (½ × 4 × 5²) = 100 + 50 = 150 m.
2. A body starts with initial velocity u = 2 m/s and accelerates uniformly at a = 14 m/s² for t = 8 s. Using s = ut + ½at², calculate the distance travelled.
464 m
s = (2 × 8) + (½ × 14 × 8²) = 16 + 448 = 464 m.
3. A body starts with initial velocity u = 7 m/s and accelerates uniformly at a = 10 m/s² for t = 8 s. Using s = ut + ½at², calculate the distance travelled.
376 m
s = (7 × 8) + (½ × 10 × 8²) = 56 + 320 = 376 m.
4. A body starts with initial velocity u = 8 m/s and accelerates uniformly at a = 4 m/s² for t = 3 s. Using s = ut + ½at², calculate the distance travelled.
42 m
s = (8 × 3) + (½ × 4 × 3²) = 24 + 18 = 42 m.
5. A body starts with initial velocity u = 19 m/s and accelerates uniformly at a = 10 m/s² for t = 5 s. Using s = ut + ½at², calculate the distance travelled.
220 m
s = (19 × 5) + (½ × 10 × 5²) = 95 + 125 = 220 m.
6. A body starts with initial velocity u = 8 m/s and accelerates uniformly at a = 16 m/s² for t = 9 s. Using s = ut + ½at², calculate the distance travelled.
720 m
s = (8 × 9) + (½ × 16 × 9²) = 72 + 648 = 720 m.
7. A body starts with initial velocity u = 13 m/s and accelerates uniformly at a = 14 m/s² for t = 2 s. Using s = ut + ½at², calculate the distance travelled.
54 m
s = (13 × 2) + (½ × 14 × 2²) = 26 + 28 = 54 m.
8. A body starts with initial velocity u = 7 m/s and accelerates uniformly at a = 4 m/s² for t = 8 s. Using s = ut + ½at², calculate the distance travelled.
184 m
s = (7 × 8) + (½ × 4 × 8²) = 56 + 128 = 184 m.
9. A body starts with initial velocity u = 17 m/s and accelerates uniformly at a = 2 m/s² for t = 6 s. Using s = ut + ½at², calculate the distance travelled.
138 m
s = (17 × 6) + (½ × 2 × 6²) = 102 + 36 = 138 m.
10. A body starts with initial velocity u = 12 m/s and accelerates uniformly at a = 2 m/s² for t = 3 s. Using s = ut + ½at², calculate the distance travelled.
45 m
s = (12 × 3) + (½ × 2 × 3²) = 36 + 9 = 45 m.
11. A body starts with initial velocity u = 14 m/s and accelerates uniformly at a = 14 m/s² for t = 3 s. Using s = ut + ½at², calculate the distance travelled.
105 m
s = (14 × 3) + (½ × 14 × 3²) = 42 + 63 = 105 m.
12. A body starts with initial velocity u = 4 m/s and accelerates uniformly at a = 10 m/s² for t = 2 s. Using s = ut + ½at², calculate the distance travelled.
28 m
s = (4 × 2) + (½ × 10 × 2²) = 8 + 20 = 28 m.

12 questions · Seed 43 · 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 = 20 m/s and accelerates uniformly at a = 4 m/s² for t = 5 s. Using s = ut + ½at², calculate the distance travelled.
u = 20 m/s, a = 4 m/s² → t = 5 s → s = ? · s = ut + ½at²
2. A body starts with initial velocity u = 2 m/s and accelerates uniformly at a = 14 m/s² for t = 8 s. Using s = ut + ½at², calculate the distance travelled.
u = 2 m/s, a = 14 m/s² → t = 8 s → s = ? · s = ut + ½at²
3. A body starts with initial velocity u = 7 m/s and accelerates uniformly at a = 10 m/s² for t = 8 s. Using s = ut + ½at², calculate the distance travelled.
u = 7 m/s, a = 10 m/s² → t = 8 s → s = ? · s = ut + ½at²
4. A body starts with initial velocity u = 8 m/s and accelerates uniformly at a = 4 m/s² for t = 3 s. Using s = ut + ½at², calculate the distance travelled.
u = 8 m/s, a = 4 m/s² → t = 3 s → s = ? · s = ut + ½at²
5. A body starts with initial velocity u = 19 m/s and accelerates uniformly at a = 10 m/s² for t = 5 s. Using s = ut + ½at², calculate the distance travelled.
u = 19 m/s, a = 10 m/s² → t = 5 s → s = ? · s = ut + ½at²
6. A body starts with initial velocity u = 8 m/s and accelerates uniformly at a = 16 m/s² for t = 9 s. Using s = ut + ½at², calculate the distance travelled.
u = 8 m/s, a = 16 m/s² → t = 9 s → s = ? · s = ut + ½at²
7. A body starts with initial velocity u = 13 m/s and accelerates uniformly at a = 14 m/s² for t = 2 s. Using s = ut + ½at², calculate the distance travelled.
u = 13 m/s, a = 14 m/s² → t = 2 s → s = ? · s = ut + ½at²
8. A body starts with initial velocity u = 7 m/s and accelerates uniformly at a = 4 m/s² for t = 8 s. Using s = ut + ½at², calculate the distance travelled.
u = 7 m/s, a = 4 m/s² → t = 8 s → s = ? · s = ut + ½at²
9. A body starts with initial velocity u = 17 m/s and accelerates uniformly at a = 2 m/s² for t = 6 s. Using s = ut + ½at², calculate the distance travelled.
u = 17 m/s, a = 2 m/s² → t = 6 s → s = ? · s = ut + ½at²
10. A body starts with initial velocity u = 12 m/s and accelerates uniformly at a = 2 m/s² for t = 3 s. Using s = ut + ½at², calculate the distance travelled.
u = 12 m/s, a = 2 m/s² → t = 3 s → s = ? · s = ut + ½at²
11. A body starts with initial velocity u = 14 m/s and accelerates uniformly at a = 14 m/s² for t = 3 s. Using s = ut + ½at², calculate the distance travelled.
u = 14 m/s, a = 14 m/s² → t = 3 s → s = ? · s = ut + ½at²
12. A body starts with initial velocity u = 4 m/s and accelerates uniformly at a = 10 m/s² for t = 2 s. Using s = ut + ½at², calculate the distance travelled.
u = 4 m/s, a = 10 m/s² → t = 2 s → s = ? · s = ut + ½at²

12 questions · Seed 43 · 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 = 20 m/s and accelerates uniformly at a = 4 m/s² for t = 5 s. Using s = ut + ½at², calculate the distance travelled.
150 m
s = (20 × 5) + (½ × 4 × 5²) = 100 + 50 = 150 m.
2. A body starts with initial velocity u = 2 m/s and accelerates uniformly at a = 14 m/s² for t = 8 s. Using s = ut + ½at², calculate the distance travelled.
464 m
s = (2 × 8) + (½ × 14 × 8²) = 16 + 448 = 464 m.
3. A body starts with initial velocity u = 7 m/s and accelerates uniformly at a = 10 m/s² for t = 8 s. Using s = ut + ½at², calculate the distance travelled.
376 m
s = (7 × 8) + (½ × 10 × 8²) = 56 + 320 = 376 m.
4. A body starts with initial velocity u = 8 m/s and accelerates uniformly at a = 4 m/s² for t = 3 s. Using s = ut + ½at², calculate the distance travelled.
42 m
s = (8 × 3) + (½ × 4 × 3²) = 24 + 18 = 42 m.
5. A body starts with initial velocity u = 19 m/s and accelerates uniformly at a = 10 m/s² for t = 5 s. Using s = ut + ½at², calculate the distance travelled.
220 m
s = (19 × 5) + (½ × 10 × 5²) = 95 + 125 = 220 m.
6. A body starts with initial velocity u = 8 m/s and accelerates uniformly at a = 16 m/s² for t = 9 s. Using s = ut + ½at², calculate the distance travelled.
720 m
s = (8 × 9) + (½ × 16 × 9²) = 72 + 648 = 720 m.
7. A body starts with initial velocity u = 13 m/s and accelerates uniformly at a = 14 m/s² for t = 2 s. Using s = ut + ½at², calculate the distance travelled.
54 m
s = (13 × 2) + (½ × 14 × 2²) = 26 + 28 = 54 m.
8. A body starts with initial velocity u = 7 m/s and accelerates uniformly at a = 4 m/s² for t = 8 s. Using s = ut + ½at², calculate the distance travelled.
184 m
s = (7 × 8) + (½ × 4 × 8²) = 56 + 128 = 184 m.
9. A body starts with initial velocity u = 17 m/s and accelerates uniformly at a = 2 m/s² for t = 6 s. Using s = ut + ½at², calculate the distance travelled.
138 m
s = (17 × 6) + (½ × 2 × 6²) = 102 + 36 = 138 m.
10. A body starts with initial velocity u = 12 m/s and accelerates uniformly at a = 2 m/s² for t = 3 s. Using s = ut + ½at², calculate the distance travelled.
45 m
s = (12 × 3) + (½ × 2 × 3²) = 36 + 9 = 45 m.
11. A body starts with initial velocity u = 14 m/s and accelerates uniformly at a = 14 m/s² for t = 3 s. Using s = ut + ½at², calculate the distance travelled.
105 m
s = (14 × 3) + (½ × 14 × 3²) = 42 + 63 = 105 m.
12. A body starts with initial velocity u = 4 m/s and accelerates uniformly at a = 10 m/s² for t = 2 s. Using s = ut + ½at², calculate the distance travelled.
28 m
s = (4 × 2) + (½ × 10 × 2²) = 8 + 20 = 28 m.

12 questions · Seed 43 · Age guidance, not curriculum certification