Acceleration Worksheet With Answers Pdf - Fill Online, Printable ... - Free Printable

Let’s solve each problem one by one. I’ll show all the steps clearly so you can follow along and understand how to get the answer.

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Problem 1:
> Heather and Matthew walk eastward with a speed of 0.98 m/s for 34 minutes. What is their displacement?

Displacement = velocity × time
But time must be in seconds because velocity is in m/s.

Convert 34 minutes to seconds:
34 min × 60 s/min = 2040 seconds

Now multiply:
Displacement = 0.98 m/s × 2040 s =
Let’s calculate:
0.98 × 2000 = 1960
0.98 × 40 = 39.2
Total = 1960 + 39.2 = 1999.2 meters

Since they’re walking east, displacement is 1999.2 m east

✔ Final Answer for #1: 1999.2 m east

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Problem 2:
> It takes you 9.5 minutes to walk with an average velocity of 1.2 m/s to the north from the bus stop to the museum entrance. What is your displacement?

Again, convert time to seconds:
9.5 min × 60 = 570 seconds

Displacement = velocity × time = 1.2 m/s × 570 s

Calculate:
1.2 × 500 = 600
1.2 × 70 = 84
Total = 600 + 84 = 684 meters

Direction is north → 684 m north

✔ Final Answer for #2: 684 m north

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Problem 3:
> Simpson drives his car with an average velocity of 24.0 m/s toward the east. How long will it take him to drive 560 km on a perfectly straight highway?

First, convert 560 km to meters:
560 km = 560 × 1000 = 560,000 meters

Time = distance ÷ velocity
Time = 560,000 m ÷ 24.0 m/s

Calculate:
560,000 ÷ 24 = ?

Let’s divide step by step:
24 × 23,000 = 552,000
Subtract: 560,000 - 552,000 = 8,000
24 × 333.33 ≈ 8,000 (since 24 × 333 = 7992)

So total time ≈ 23,000 + 333.33 = 23,333.33 seconds

We can also write as fraction:
560,000 ÷ 24 = 560,000 / 24 = simplify by dividing numerator and denominator by 8:
= 70,000 / 3 ≈ 23,333.33 seconds

If we want in hours or minutes? The question doesn’t specify, so leave in seconds unless told otherwise. But let’s check — maybe they expect hours?

Wait — 23,333 seconds is a lot. Let’s convert to hours to see if it makes sense:

23,333.33 ÷ 3600 ≈ 6.48 hours — that seems reasonable for 560 km at 24 m/s (which is about 86.4 km/h).

But since the question didn’t ask for specific units, and input was in m/s and km, probably best to give answer in seconds OR convert to more useful unit.

Actually, let’s re-read: “How long will it take” — no unit specified. In physics problems like this, if not specified, use SI units — seconds.

But 23,333 seconds is correct mathematically.

Alternatively, maybe they expect it in hours? Let me double-check calculation.

Velocity = 24 m/s = 24 × 3600 = 86,400 m/h = 86.4 km/h

Distance = 560 km

Time = 560 / 86.4 ≈ ?

560 ÷ 86.4:

86.4 × 6 = 518.4
560 - 518.4 = 41.6
41.6 / 86.4 ≈ 0.481

So ≈ 6.481 hours

But again, unless asked, stick to seconds.

However, looking back at problem 1 and 2, they used minutes and converted to seconds — so likely expect seconds here too.

But 23,333.33 seconds is exact? Let’s do exact division:

560,000 ÷ 24 = 560000 / 24 = reduce fraction:

Divide numerator and denominator by 8: 70000 / 3 = 23333⅓ seconds

So we can write as 23333.33 s or 70000/3 s

I think decimal is fine.

✔ Final Answer for #3: 23333.33 seconds

*(Note: If teacher expects hours, it would be ~6.48 h, but based on context, seconds are appropriate.)*

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Problem 4:
> Marissa’s car accelerates at a rate of 2.90 m/s². How long does it take for Marissa’s car to accelerate from a velocity of 24.6 m/s to a velocity of 26.8 m/s?

Use formula:
v = u + at
Where:
v = final velocity = 26.8 m/s
u = initial velocity = 24.6 m/s
a = acceleration = 2.90 m/s²
t = ?

Rearrange: t = (v - u) / a

t = (26.8 - 24.6) / 2.90 = 2.2 / 2.90

Calculate:
2.2 ÷ 2.90 = ?

Multiply numerator and denominator by 100: 220 / 290 = 22/29 ≈ 0.7586...

So approximately 0.759 seconds

Let me compute exactly:
2.2 ÷ 2.9 = 22 ÷ 29 = 0.758620689... → round to 3 sig figs? Inputs have 3 sig figs (2.90, 24.6, 26.8) → so answer should have 3 sig figs.

2.2 has 2 sig figs? Wait — 26.8 - 24.6 = 2.2 → which has 2 sig figs? Actually, subtraction: both have one decimal place, so difference has one decimal place → 2.2 is precise to tenths.

Acceleration is 2.90 → three sig figs.

In division, least number of sig figs determines answer. Here, 2.2 has 2 sig figs, 2.90 has 3 → so answer should have 2 sig figs.

2.2 / 2.90 = 0.7586 → rounded to 2 sig figs = 0.76 seconds

✔ Final Answer for #4: 0.76 seconds

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Problem 5:
> Turnip jumped up with a velocity of -1.2 m/s. After 25 minutes, he reached a velocity of -4.5 m/s. What is the acceleration of this turnip during the 25-minute interval?

Acceleration = change in velocity / time

Δv = v_final - v_initial = (-4.5) - (-1.2) = -4.5 + 1.2 = -3.3 m/s

Time = 25 minutes → convert to seconds: 25 × 60 = 1500 seconds

a = Δv / t = -3.3 / 1500 = ?

Calculate:
-3.3 ÷ 1500 = -0.0022 m/s²

Or in scientific notation: -2.2 × 10⁻³ m/s²

Check sig figs: velocities given to 2 sig figs (-1.2, -4.5), time 25 min → 2 sig figs? 25 could be exact, but usually treated as 2 sig figs.

So answer should have 2 sig figs: -0.0022 m/s² or -2.2 × 10⁻³ m/s²

✔ Final Answer for #5: -0.0022 m/s²

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Problem 6:
> A car accelerates from rest at 3.00 m/s². What is the velocity at the end of 7.3 seconds?

Rest means initial velocity u = 0

v = u + at = 0 + (3.00)(7.3) = ?

3.00 × 7.3 = 21.9

Sig figs: 3.00 has 3, 7.3 has 2 → so answer should have 2 sig figs → 22 m/s

Wait — 7.3 has two sig figs, 3.00 has three → product should have two sig figs.

21.9 rounded to two sig figs is 22 m/s

✔ Final Answer for #6: 22 m/s

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Problem 7:
> As the shuttle bus comes to a sudden stop to avoid hitting a dog, it accelerates uniformly at -4.1 m/s² as it slows from 9.0 m/s to 0 m/s. Find the time it takes the bus to come to a complete stop.

Use: v = u + at

v = 0, u = 9.0 m/s, a = -4.1 m/s²

0 = 9.0 + (-4.1)t
→ 0 = 9.0 - 4.1t
→ 4.1t = 9.0
→ t = 9.0 / 4.1 ≈ ?

9.0 ÷ 4.1 = 2.195... → round to 2 sig figs? 9.0 has 2, 4.1 has 2 → so answer 2.2 seconds

✔ Final Answer for #7: 2.2 seconds

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Problem 8:
> Nathan accelerates his skateboard along a straight path from rest to 12.5 m/s in 2.5 seconds. What is Nathan’s acceleration?

a = (v - u) / t = (12.5 - 0) / 2.5 = 12.5 / 2.5 = 5.0 m/s²

Sig figs: 12.5 has 3, 2.5 has 2 → so answer should have 2 sig figs → 5.0 m/s² (already has 2)

✔ Final Answer for #8: 5.0 m/s²

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## Final Answers:

1. 1999.2 m east
2. 684 m north
3. 23333.33 seconds
4. 0.76 seconds
5. -0.0022 m/s²
6. 22 m/s
7. 2.2 seconds
8. 5.0 m/s²