Worksheet titled "Acceleration Calculations" featuring six word problems related to physics, with a table for answers.
Acceleration Calculations worksheet with problems and table for solutions.
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Step-by-step solution for: Acceleration worksheet.pdf - Acceleration Calculations 1. Change ...
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Show Answer Key & Explanations
Step-by-step solution for: Acceleration worksheet.pdf - Acceleration Calculations 1. Change ...
Let’s solve each problem one by one. We’ll use the formula for acceleration:
Acceleration = (Final Speed – Initial Speed) ÷ Time
We’ll write it as:
a = (v_f - v_i) / t
Where:
- a = acceleration
- v_f = final speed
- v_i = initial speed
- t = time
---
Problem 1:
Change in speed = 14 m/s, time taken = 2 seconds.
Since “change in speed” means (final – initial), we can plug directly into the formula:
a = 14 m/s ÷ 2 s = 7 m/s²
✔ Check: 14 divided by 2 is 7. Units are m/s per second → m/s². Correct.
---
Problem 2:
Initial speed = 0 m/s (starts from rest), final speed = 30 m/s, time = 3 seconds.
a = (30 - 0) / 3 = 30 / 3 = 10 m/s²
✔ Check: 30 divided by 3 is 10. Makes sense — speeding up fast!
---
Problem 3:
Initial speed = 20 m/s, final speed = 50 m/s, time = 3 seconds.
a = (50 - 20) / 3 = 30 / 3 = 10 m/s²
✔ Check: Same as above — 30 over 3 is 10. Good.
---
Problem 4:
Car slows down from 50 m/s to 30 m/s in 10 seconds.
So initial = 50, final = 30, time = 10.
a = (30 - 50) / 10 = (-20) / 10 = -2 m/s²
✔ Check: Negative sign means slowing down — that’s deceleration. Correct.
---
Problem 5:
Roller coaster: initial = 10 m/s, final = 26 m/s, time = 2 seconds.
a = (26 - 10) / 2 = 16 / 2 = 8 m/s²
✔ Check: 16 divided by 2 is 8. Simple and right.
---
Problem 6:
Ball rolling down ramp: starts at 0.8 m/s, ends at 7 m/s, time = 15 seconds.
a = (7 - 0.8) / 15 = 6.2 / 15
Let’s calculate that:
6.2 ÷ 15 = ?
Do division:
15 × 0.4 = 6.0 → remainder 0.2
0.2 ÷ 15 = 0.0133...
So total ≈ 0.4133...
But let’s keep it exact:
6.2 / 15 = 62/150 = 31/75 ≈ 0.413 m/s²
Wait — maybe better to leave as decimal rounded to 3 places? Or fraction?
Actually, 6.2 ÷ 15 = 0.413333... so we can say ≈ 0.413 m/s²
But let me double-check:
15 × 0.413 = 15×0.4=6, 15×0.013=0.195 → total 6.195 → close to 6.2. OK.
Alternatively, if we want exact value:
6.2 / 15 = 62/150 = 31/75 m/s² — but probably decimal is fine.
I think for school level, rounding to 3 significant figures or 2 decimals is okay.
6.2 has 2 sig figs, 15 has 2 → answer should have 2 sig figs?
6.2 ÷ 15 = 0.41333 → with 2 sig figs → 0.41 m/s²
Wait — actually, 6.2 has two sig figs, 15 also has two → quotient should have two.
0.41333… → first two non-zero digits are 4 and 1 → so 0.41 m/s²
✔ Final answer: 0.41 m/s²
---
Problem 7:
Meteoroid: initial = 1.0 km/s, final = 1.8 km/s, time = 0.03 seconds.
First, note units: km/s — but acceleration will be in km/s² unless converted. But since question doesn’t specify, we can leave in km/s².
a = (1.8 - 1.0) / 0.03 = 0.8 / 0.03
Calculate:
0.8 ÷ 0.03 = 80 ÷ 3 = 26.666... km/s²
That’s about 26.7 km/s² (rounded to 3 sig figs)
Check: 0.03 × 26.666 = 0.8 → yes.
✔ Answer: 26.7 km/s²
---
Problem 8:
Space telescope: starts at rest → initial = 0, reaches 1700 m/s in 25 seconds.
a = (1700 - 0) / 25 = 1700 / 25
Calculate:
25 × 68 = 1700 → so 68 m/s²
✔ Check: 25 × 68 = 1700. Perfect.
---
Problem 9:
Car traveling at 30 m/s, accelerates at 2 m/s² for 3 seconds. What is new speed?
Use:
Final speed = Initial speed + (acceleration × time)
v_f = v_i + a·t
v_f = 30 + (2 × 3) = 30 + 6 = 36 m/s
✔ Check: Accelerating 2 m/s every second for 3 seconds → adds 6 m/s. 30+6=36. Correct.
---
Problem 10: Complete the table.
Table has columns: Initial Speed, Final Speed, Time, Acceleration.
Row 1:
Initial = 0 m/s, Final = 10 m/s, Time = 5 s
→ a = (10 - 0)/5 = 2 m/s²
Row 2:
Initial = 10 m/s, Final = 30 m/s, Time = 4 s
→ a = (30 - 10)/4 = 20/4 = 5 m/s²
Row 3:
Initial = 20 m/s, Final = 50 m/s, Time = 3 s
→ a = (50 - 20)/3 = 30/3 = 10 m/s²
Row 4:
Initial = 50 m/s, Final = 30 m/s, Time = 10 s
→ a = (30 - 50)/10 = -20/10 = -2 m/s²
Row 5:
Initial = 0 m/s, Final = 20 m/s, Time = 4 s
→ a = (20 - 0)/4 = 20/4 = 5 m/s²
Row 6:
Initial = 15 m/s, Final = 25 m/s, Time = 2 s
→ a = (25 - 15)/2 = 10/2 = 5 m/s²
Row 7:
Initial = 30 m/s, Final = 10 m/s, Time = 5 s
→ a = (10 - 30)/5 = -20/5 = -4 m/s²
Row 8:
Initial = 0 m/s, Final = 40 m/s, Time = 8 s
→ a = (40 - 0)/8 = 40/8 = 5 m/s²
All checked.
---
Now, compiling all answers:
1. 7 m/s²
2. 10 m/s²
3. 10 m/s²
4. -2 m/s²
5. 8 m/s²
6. 0.41 m/s²
7. 26.7 km/s²
8. 68 m/s²
9. 36 m/s²
10. Table filled as above.
Final Answer:
1. 7 m/s²
2. 10 m/s²
3. 10 m/s²
4. -2 m/s²
5. 8 m/s²
6. 0.41 m/s²
7. 26.7 km/s²
8. 68 m/s²
9. 36 m/s²
10. Row 1: 2 m/s²; Row 2: 5 m/s²; Row 3: 10 m/s²; Row 4: -2 m/s²; Row 5: 5 m/s²; Row 6: 5 m/s²; Row 7: -4 m/s²; Row 8: 5 m/s²
Acceleration = (Final Speed – Initial Speed) ÷ Time
We’ll write it as:
a = (v_f - v_i) / t
Where:
- a = acceleration
- v_f = final speed
- v_i = initial speed
- t = time
---
Problem 1:
Change in speed = 14 m/s, time taken = 2 seconds.
Since “change in speed” means (final – initial), we can plug directly into the formula:
a = 14 m/s ÷ 2 s = 7 m/s²
✔ Check: 14 divided by 2 is 7. Units are m/s per second → m/s². Correct.
---
Problem 2:
Initial speed = 0 m/s (starts from rest), final speed = 30 m/s, time = 3 seconds.
a = (30 - 0) / 3 = 30 / 3 = 10 m/s²
✔ Check: 30 divided by 3 is 10. Makes sense — speeding up fast!
---
Problem 3:
Initial speed = 20 m/s, final speed = 50 m/s, time = 3 seconds.
a = (50 - 20) / 3 = 30 / 3 = 10 m/s²
✔ Check: Same as above — 30 over 3 is 10. Good.
---
Problem 4:
Car slows down from 50 m/s to 30 m/s in 10 seconds.
So initial = 50, final = 30, time = 10.
a = (30 - 50) / 10 = (-20) / 10 = -2 m/s²
✔ Check: Negative sign means slowing down — that’s deceleration. Correct.
---
Problem 5:
Roller coaster: initial = 10 m/s, final = 26 m/s, time = 2 seconds.
a = (26 - 10) / 2 = 16 / 2 = 8 m/s²
✔ Check: 16 divided by 2 is 8. Simple and right.
---
Problem 6:
Ball rolling down ramp: starts at 0.8 m/s, ends at 7 m/s, time = 15 seconds.
a = (7 - 0.8) / 15 = 6.2 / 15
Let’s calculate that:
6.2 ÷ 15 = ?
Do division:
15 × 0.4 = 6.0 → remainder 0.2
0.2 ÷ 15 = 0.0133...
So total ≈ 0.4133...
But let’s keep it exact:
6.2 / 15 = 62/150 = 31/75 ≈ 0.413 m/s²
Wait — maybe better to leave as decimal rounded to 3 places? Or fraction?
Actually, 6.2 ÷ 15 = 0.413333... so we can say ≈ 0.413 m/s²
But let me double-check:
15 × 0.413 = 15×0.4=6, 15×0.013=0.195 → total 6.195 → close to 6.2. OK.
Alternatively, if we want exact value:
6.2 / 15 = 62/150 = 31/75 m/s² — but probably decimal is fine.
I think for school level, rounding to 3 significant figures or 2 decimals is okay.
6.2 has 2 sig figs, 15 has 2 → answer should have 2 sig figs?
6.2 ÷ 15 = 0.41333 → with 2 sig figs → 0.41 m/s²
Wait — actually, 6.2 has two sig figs, 15 also has two → quotient should have two.
0.41333… → first two non-zero digits are 4 and 1 → so 0.41 m/s²
✔ Final answer: 0.41 m/s²
---
Problem 7:
Meteoroid: initial = 1.0 km/s, final = 1.8 km/s, time = 0.03 seconds.
First, note units: km/s — but acceleration will be in km/s² unless converted. But since question doesn’t specify, we can leave in km/s².
a = (1.8 - 1.0) / 0.03 = 0.8 / 0.03
Calculate:
0.8 ÷ 0.03 = 80 ÷ 3 = 26.666... km/s²
That’s about 26.7 km/s² (rounded to 3 sig figs)
Check: 0.03 × 26.666 = 0.8 → yes.
✔ Answer: 26.7 km/s²
---
Problem 8:
Space telescope: starts at rest → initial = 0, reaches 1700 m/s in 25 seconds.
a = (1700 - 0) / 25 = 1700 / 25
Calculate:
25 × 68 = 1700 → so 68 m/s²
✔ Check: 25 × 68 = 1700. Perfect.
---
Problem 9:
Car traveling at 30 m/s, accelerates at 2 m/s² for 3 seconds. What is new speed?
Use:
Final speed = Initial speed + (acceleration × time)
v_f = v_i + a·t
v_f = 30 + (2 × 3) = 30 + 6 = 36 m/s
✔ Check: Accelerating 2 m/s every second for 3 seconds → adds 6 m/s. 30+6=36. Correct.
---
Problem 10: Complete the table.
Table has columns: Initial Speed, Final Speed, Time, Acceleration.
Row 1:
Initial = 0 m/s, Final = 10 m/s, Time = 5 s
→ a = (10 - 0)/5 = 2 m/s²
Row 2:
Initial = 10 m/s, Final = 30 m/s, Time = 4 s
→ a = (30 - 10)/4 = 20/4 = 5 m/s²
Row 3:
Initial = 20 m/s, Final = 50 m/s, Time = 3 s
→ a = (50 - 20)/3 = 30/3 = 10 m/s²
Row 4:
Initial = 50 m/s, Final = 30 m/s, Time = 10 s
→ a = (30 - 50)/10 = -20/10 = -2 m/s²
Row 5:
Initial = 0 m/s, Final = 20 m/s, Time = 4 s
→ a = (20 - 0)/4 = 20/4 = 5 m/s²
Row 6:
Initial = 15 m/s, Final = 25 m/s, Time = 2 s
→ a = (25 - 15)/2 = 10/2 = 5 m/s²
Row 7:
Initial = 30 m/s, Final = 10 m/s, Time = 5 s
→ a = (10 - 30)/5 = -20/5 = -4 m/s²
Row 8:
Initial = 0 m/s, Final = 40 m/s, Time = 8 s
→ a = (40 - 0)/8 = 40/8 = 5 m/s²
All checked.
---
Now, compiling all answers:
1. 7 m/s²
2. 10 m/s²
3. 10 m/s²
4. -2 m/s²
5. 8 m/s²
6. 0.41 m/s²
7. 26.7 km/s²
8. 68 m/s²
9. 36 m/s²
10. Table filled as above.
Final Answer:
1. 7 m/s²
2. 10 m/s²
3. 10 m/s²
4. -2 m/s²
5. 8 m/s²
6. 0.41 m/s²
7. 26.7 km/s²
8. 68 m/s²
9. 36 m/s²
10. Row 1: 2 m/s²; Row 2: 5 m/s²; Row 3: 10 m/s²; Row 4: -2 m/s²; Row 5: 5 m/s²; Row 6: 5 m/s²; Row 7: -4 m/s²; Row 8: 5 m/s²
Parent Tip: Review the logic above to help your child master the concept of acceleration calculations worksheet.
