ScienceAges 16-18

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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Age band:Ages 13-15 Ages 16-18

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Worksheet StudioPractice pack · Ages 16-18

Uniform acceleration (s = ut + ½at²)

Take your time. Show your thinking.

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

12 questions · Seed 44 · Age guidance, not curriculum certification

View the answer key

Worksheet StudioAnswer key · Ages 16-18

Uniform acceleration (s = ut + ½at²)

Answers and reasoning. Review before teaching.

1. A body starts with initial velocity u = 10 m/s and accelerates uniformly at a = 2 m/s² for t = 10 s. Using s = ut + ½at², calculate the distance travelled.
200 m
s = (10 × 10) + (½ × 2 × 10²) = 100 + 100 = 200 m.
2. A body starts with initial velocity u = 4 m/s and accelerates uniformly at a = 6 m/s² for t = 5 s. Using s = ut + ½at², calculate the distance travelled.
95 m
s = (4 × 5) + (½ × 6 × 5²) = 20 + 75 = 95 m.
3. A body starts with initial velocity u = 18 m/s and accelerates uniformly at a = 6 m/s² for t = 6 s. Using s = ut + ½at², calculate the distance travelled.
216 m
s = (18 × 6) + (½ × 6 × 6²) = 108 + 108 = 216 m.
4. A body starts with initial velocity u = 4 m/s and accelerates uniformly at a = 16 m/s² for t = 5 s. Using s = ut + ½at², calculate the distance travelled.
220 m
s = (4 × 5) + (½ × 16 × 5²) = 20 + 200 = 220 m.
5. A body starts with initial velocity u = 16 m/s and accelerates uniformly at a = 14 m/s² for t = 8 s. Using s = ut + ½at², calculate the distance travelled.
576 m
s = (16 × 8) + (½ × 14 × 8²) = 128 + 448 = 576 m.
6. A body starts with initial velocity u = 16 m/s and accelerates uniformly at a = 4 m/s² for t = 7 s. Using s = ut + ½at², calculate the distance travelled.
210 m
s = (16 × 7) + (½ × 4 × 7²) = 112 + 98 = 210 m.
7. A body starts with initial velocity u = 4 m/s and accelerates uniformly at a = 6 m/s² for t = 8 s. Using s = ut + ½at², calculate the distance travelled.
224 m
s = (4 × 8) + (½ × 6 × 8²) = 32 + 192 = 224 m.
8. A body starts with initial velocity u = 15 m/s and accelerates uniformly at a = 8 m/s² for t = 8 s. Using s = ut + ½at², calculate the distance travelled.
376 m
s = (15 × 8) + (½ × 8 × 8²) = 120 + 256 = 376 m.
9. A body starts with initial velocity u = 12 m/s and accelerates uniformly at a = 4 m/s² for t = 9 s. Using s = ut + ½at², calculate the distance travelled.
270 m
s = (12 × 9) + (½ × 4 × 9²) = 108 + 162 = 270 m.
10. A body starts with initial velocity u = 12 m/s and accelerates uniformly at a = 6 m/s² for t = 5 s. Using s = ut + ½at², calculate the distance travelled.
135 m
s = (12 × 5) + (½ × 6 × 5²) = 60 + 75 = 135 m.
11. A body starts with initial velocity u = 14 m/s and accelerates uniformly at a = 8 m/s² for t = 4 s. Using s = ut + ½at², calculate the distance travelled.
120 m
s = (14 × 4) + (½ × 8 × 4²) = 56 + 64 = 120 m.
12. A body starts with initial velocity u = 9 m/s and accelerates uniformly at a = 4 m/s² for t = 6 s. Using s = ut + ½at², calculate the distance travelled.
126 m
s = (9 × 6) + (½ × 4 × 6²) = 54 + 72 = 126 m.

12 questions · Seed 44 · Age guidance, not curriculum certification

Worksheet StudioPractice pack · Ages 16-18

Uniform acceleration (s = ut + ½at²)

Take your time. Show your thinking.

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

12 questions · Seed 44 · Age guidance, not curriculum certification

Worksheet StudioAnswer key · Ages 16-18

Uniform acceleration (s = ut + ½at²)

Answers and reasoning. Review before teaching.

1. A body starts with initial velocity u = 10 m/s and accelerates uniformly at a = 2 m/s² for t = 10 s. Using s = ut + ½at², calculate the distance travelled.
200 m
s = (10 × 10) + (½ × 2 × 10²) = 100 + 100 = 200 m.
2. A body starts with initial velocity u = 4 m/s and accelerates uniformly at a = 6 m/s² for t = 5 s. Using s = ut + ½at², calculate the distance travelled.
95 m
s = (4 × 5) + (½ × 6 × 5²) = 20 + 75 = 95 m.
3. A body starts with initial velocity u = 18 m/s and accelerates uniformly at a = 6 m/s² for t = 6 s. Using s = ut + ½at², calculate the distance travelled.
216 m
s = (18 × 6) + (½ × 6 × 6²) = 108 + 108 = 216 m.
4. A body starts with initial velocity u = 4 m/s and accelerates uniformly at a = 16 m/s² for t = 5 s. Using s = ut + ½at², calculate the distance travelled.
220 m
s = (4 × 5) + (½ × 16 × 5²) = 20 + 200 = 220 m.
5. A body starts with initial velocity u = 16 m/s and accelerates uniformly at a = 14 m/s² for t = 8 s. Using s = ut + ½at², calculate the distance travelled.
576 m
s = (16 × 8) + (½ × 14 × 8²) = 128 + 448 = 576 m.
6. A body starts with initial velocity u = 16 m/s and accelerates uniformly at a = 4 m/s² for t = 7 s. Using s = ut + ½at², calculate the distance travelled.
210 m
s = (16 × 7) + (½ × 4 × 7²) = 112 + 98 = 210 m.
7. A body starts with initial velocity u = 4 m/s and accelerates uniformly at a = 6 m/s² for t = 8 s. Using s = ut + ½at², calculate the distance travelled.
224 m
s = (4 × 8) + (½ × 6 × 8²) = 32 + 192 = 224 m.
8. A body starts with initial velocity u = 15 m/s and accelerates uniformly at a = 8 m/s² for t = 8 s. Using s = ut + ½at², calculate the distance travelled.
376 m
s = (15 × 8) + (½ × 8 × 8²) = 120 + 256 = 376 m.
9. A body starts with initial velocity u = 12 m/s and accelerates uniformly at a = 4 m/s² for t = 9 s. Using s = ut + ½at², calculate the distance travelled.
270 m
s = (12 × 9) + (½ × 4 × 9²) = 108 + 162 = 270 m.
10. A body starts with initial velocity u = 12 m/s and accelerates uniformly at a = 6 m/s² for t = 5 s. Using s = ut + ½at², calculate the distance travelled.
135 m
s = (12 × 5) + (½ × 6 × 5²) = 60 + 75 = 135 m.
11. A body starts with initial velocity u = 14 m/s and accelerates uniformly at a = 8 m/s² for t = 4 s. Using s = ut + ½at², calculate the distance travelled.
120 m
s = (14 × 4) + (½ × 8 × 4²) = 56 + 64 = 120 m.
12. A body starts with initial velocity u = 9 m/s and accelerates uniformly at a = 4 m/s² for t = 6 s. Using s = ut + ½at², calculate the distance travelled.
126 m
s = (9 × 6) + (½ × 4 × 6²) = 54 + 72 = 126 m.

12 questions · Seed 44 · Age guidance, not curriculum certification