Linear Motion Exercise | PDF | Acceleration | Classical Mechanics - Free Printable

Let's solve each problem on the Linear Motion Worksheet using the K-U-E-S method:

---

K = Knowns

U = Unknowns
E = Equation
S = Substitute & Solve

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## SPEED

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1. Light from the sun reaches the earth in 498 s. If the sun is 1.494 × 10¹¹ m from the earth, how fast (m/s) does light travel in space?

#### K:
- Distance: $ d = 1.494 \times 10^{11} \text{ m} $
- Time: $ t = 498 \text{ s} $

#### U:
- Speed of light: $ v = ? $

#### E:
$$
v = \frac{d}{t}
$$

#### S:
$$
v = \frac{1.494 \times 10^{11}}{498} = 3.00 \times 10^8 \text{ m/s}
$$

✔ Answer: $ \boxed{3.00 \times 10^8 \text{ m/s}} $

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2. A bullet is fired at 660 m/s and strikes a target 200.0 meters away. What is the duration of the bullet’s flight?

#### K:
- Speed: $ v = 660 \text{ m/s} $
- Distance: $ d = 200.0 \text{ m} $

#### U:
- Time: $ t = ? $

#### E:
$$
t = \frac{d}{v}
$$

#### S:
$$
t = \frac{200.0}{660} = 0.3030... \approx 0.30 \text{ s}
$$

✔ Answer: $ \boxed{0.30 \text{ s}} $

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3. What is the average speed (km/h and m/h) of a runner who completes a 5.00 km race in 20.50 min?

#### K:
- Distance: $ d = 5.00 \text{ km} $
- Time: $ t = 20.50 \text{ min} $

Convert time to hours:
$$
t = \frac{20.50}{60} = 0.3417 \text{ h}
$$

#### U:
- Average speed: $ v = ? $ (in km/h and m/h)

#### E:
$$
v = \frac{d}{t}
$$

#### S:
- In km/h:
$$
v = \frac{5.00}{0.3417} = 14.63 \approx 14.6 \text{ km/h}
$$

Now convert to m/h:
- $ 5.00 \text{ km} = 5000 \text{ m} $
- $ 20.50 \text{ min} = 20.50 \times 60 = 1230 \text{ s} $
But we want m/h, so use:
$$
v = \frac{5000 \text{ m}}{0.3417 \text{ h}} = 14630 \text{ m/h} \approx 1.46 \times 10^4 \text{ m/h}
$$

Wait — but let’s do it properly.

Actually:
$$
\text{Speed in m/h} = \left( \frac{5000 \text{ m}}{20.50 \text{ min}} \right) \times 60 \text{ min/h} = \frac{5000}{20.50} \times 60 = 243.9 \times 60 = 14634 \text{ m/h}
$$

So:
- $ v = 14.6 \text{ km/h} $
- $ v = 1.46 \times 10^4 \text{ m/h} $

But the answer key says 14.6 km/h and 9.05 m/h → That can't be right.

Wait — 9.05 m/h is way too slow. Let’s double-check.

Ah! There might be a mistake in interpretation.

Wait — is the question asking for m/h or m/s?

No — it says km/h and m/h.

But 9.05 m/h is about 0.0025 m/s — impossible for a runner.

Let’s recheck:

- Distance: 5.00 km = 5000 m
- Time: 20.50 min = 1230 seconds

Average speed in m/s:
$$
v = \frac{5000}{1230} = 4.065 \text{ m/s}
$$

Now convert to m/h:
$$
4.065 \text{ m/s} \times 3600 \text{ s/h} = 14,634 \text{ m/h} \approx 1.46 \times 10^4 \text{ m/h}
$$

And km/h:
$$
5.00 \text{ km} / (20.50/60) \text{ h} = 5.00 / 0.3417 = 14.63 \text{ km/h}
$$

So correct answers are:
- $ \boxed{14.6 \text{ km/h}} $
- $ \boxed{1.46 \times 10^4 \text{ m/h}} $

But the answer key says 14.6 km/h and 9.05 m/h — that must be a typo.

Wait — maybe they meant m/s, not m/h?

Check: $ 9.05 \text{ m/s} $? No, 9.05 m/s is faster than sprinters.

Wait — 5 km in 20.5 min:
- 20.5 min = 1230 s
- 5000 m / 1230 s ≈ 4.065 m/s

So 4.065 m/s → not 9.05.

Wait — perhaps the answer key has a typo, or I misread.

Wait — the answer key says 9.05 m/h — that’s clearly wrong.

But let’s look again.

Wait — maybe the answer key meant 9.05 m/s? But no, 9.05 m/s is 32.6 km/h — very fast.

Alternatively, perhaps they meant m/min?

Let’s see:
- 5000 m / 20.50 min = 243.9 m/min

Still not 9.05.

Wait — could it be m/s?

No — 5000 / 1230 = ~4.06 m/s

Hmm.

Wait — maybe the answer key is wrong, or there’s a misunderstanding.

But the correct answer should be:

✔ Answer:
$ \boxed{14.6 \text{ km/h}} $ and $ \boxed{1.46 \times 10^4 \text{ m/h}} $

But since the answer key says 9.05 m/h, which is incorrect, likely a typo.

Wait — unless the race was 5.00 km in 20.50 hours? No, that would be absurd.

No — 20.50 min is correct.

So I think the answer key has a typo. The correct value is ~14,600 m/h, not 9.05.

But wait — 9.05 m/h is about 0.0025 m/s — like a snail.

So definitely wrong.

We’ll go with correct values.

✔ Final Answer:
Speed = $ \boxed{14.6 \text{ km/h}} $ and $ \boxed{1.46 \times 10^4 \text{ m/h}} $

---

4. How far would an object move in 20.0 seconds if it were traveling at a constant speed of 63.00 meters per second?

#### K:
- Speed: $ v = 63.00 \text{ m/s} $
- Time: $ t = 20.0 \text{ s} $

#### U:
- Distance: $ d = ? $

#### E:
$$
d = v \cdot t
$$

#### S:
$$
d = 63.00 \times 20.0 = 1260 \text{ m}
$$

✔ Answer: $ \boxed{1260 \text{ m}} $

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5. An amusement park carousel travels at a speed of 8.0 m/s. If the circular track of the carousel has a radius of 10.3 m, how many seconds will it take for the carousel to make one complete revolution?

#### K:
- Speed: $ v = 8.0 \text{ m/s} $
- Radius: $ r = 10.3 \text{ m} $

#### U:
- Time for one revolution: $ T = ? $

#### E:
- Circumference: $ C = 2\pi r $
- $ v = \frac{d}{t} \Rightarrow t = \frac{d}{v} = \frac{2\pi r}{v} $

#### S:
$$
C = 2\pi(10.3) = 64.73 \text{ m}
$$
$$
T = \frac{64.73}{8.0} = 8.09 \text{ s} \approx 8.1 \text{ s}
$$

✔ Answer: $ \boxed{8.1 \text{ s}} $

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## VELOCITY

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6. What is the velocity of a car traveling north on I-75 if it takes 2 hours to reach Chattanooga (120 miles)?

#### K:
- Distance: $ d = 120 \text{ miles} $
- Time: $ t = 2 \text{ h} $
- Direction: North

#### U:
- Velocity: $ v = ? $ (magnitude and direction)

#### E:
$$
v = \frac{d}{t}
$$

#### S:
$$
v = \frac{120}{2} = 60 \text{ mi/h}
$$

Direction: North

✔ Answer: $ \boxed{60 \text{ mi/h N}} $

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7. The controls on a motorboat are marked at the position where it travels at 25.0 km/h in still water. What will be the velocity of the boat, as measured by an observer on shore, if it is directed upstream on a river which flows at the rate of 4.0 km/h?

#### K:
- Boat speed in still water: $ v_b = 25.0 \text{ km/h} $
- River current: $ v_r = 4.0 \text{ km/h} $ downstream
- Boat going upstream → opposite to current

#### U:
- Velocity of boat relative to shore: $ v_{bs} = ? $

#### E:
$$
v_{bs} = v_b - v_r \quad \text{(since upstream)}
$$

#### S:
$$
v_{bs} = 25.0 - 4.0 = 21.0 \text{ km/h}
$$

Direction: Upstream (same as boat)

✔ Answer: $ \boxed{21.0 \text{ km/h}} $ (upstream)

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✔ Summary of Answers:

| Problem | Answer |
|--------|--------|
| 1 | $ 3.00 \times 10^8 \text{ m/s} $ |
| 2 | $ 0.30 \text{ s} $ |
| 3 | $ 14.6 \text{ km/h},\ 1.46 \times 10^4 \text{ m/h} $ *(Note: 9.05 m/h in key is likely a typo)* |
| 4 | $ 1260 \text{ m} $ |
| 5 | $ 8.1 \text{ s} $ |
| 6 | $ 60 \text{ mi/h N} $ |
| 7 | $ 21.0 \text{ km/h} $ |

All solved using K-U-E-S method.

Let me know if you'd like these formatted neatly for printing or submission!