Completed Distance and Displacement Lab worksheet with student measurements and calculations.

Let's go through the Distance and Displacement Lab step by step, analyze the data provided, correct any inconsistencies, and explain how to solve each part properly.

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🔹 Important Notes:

- The lab asks to round all measurements to the nearest meter, but many values are in centimeters (cm). We’ll convert them to meters (m) for consistency.
- Distance = total path traveled (scalar quantity).
- Displacement = straight-line distance from start to end point (vector quantity), including direction.

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## ✔ Activity #1

Step-by-step:

1. Origin: Marked with tape.

2. Walk 10 steps forward:
- Measured distance: 325 cm = 3.25 m → Rounded to 3 m
*(Note: The instruction says round to nearest meter, so we'll use 3 m)*

3. Turn 180°, walk 5 steps backward:
- Measured distance: 165 cm = 1.65 m → Rounded to 2 m

4. Turn 180° again, walk 20 steps forward:
- Measured distance: 638 cm = 6.38 m → Rounded to 6 m

5. Final measured displacement from origin:
- Measured: 225 cm = 2.25 m → Rounded to 2 m

6. Now calculate:

#### ➤ Total Distance Traveled:
Add all distances walked:
- Forward: 3 m + 6 m = 9 m
- Backward: 2 m
- Total distance = 3 + 2 + 6 = 11 m

> But the student wrote 1.128 cm — this is clearly a mistake (units and magnitude).
> Likely they meant 1128 cm = 11.28 m, which rounds to 11 m.

✔ So, Distance = 11 m

#### ➤ Calculated Displacement:
We consider direction:
- Forward: +3 m
- Then back: –2 m
- Then forward again: +6 m

Total displacement = 3 – 2 + 6 = 7 m forward

But the student wrote 792 cm = 7.92 m → This is close, but not matching our calculation.

Wait — let’s check their numbers:
- 325 cm = 3.25 m
- 165 cm = 1.65 m
- 638 cm = 6.38 m

So actual displacement:
- Forward: 3.25 m
- Backward: –1.65 m
- Forward again: +6.38 m

Net displacement = 3.25 – 1.65 + 6.38 = 7.98 m ≈ 8 m

But measured displacement was 225 cm = 2.25 m → That doesn’t match!

⚠️ Problem: There’s a huge discrepancy between calculated displacement (~8 m) and measured displacement (2.25 m).

This suggests either:
- Measurement error,
- Or misunderstanding of directions.

Let’s re-analyze the path:

- Start at origin.
- Walk 10 steps forward → 3.25 m
- Turn 180° → now facing opposite direction
- Walk 5 steps → 1.65 m backward → position: 3.25 – 1.65 = 1.60 m from origin
- Turn 180° again → now facing original direction
- Walk 20 steps → 6.38 m forward → new position: 1.60 + 6.38 = 7.98 m from origin

So final position should be about 8 m forward.

But the student measured only 2.25 m from origin? That can't be right unless the path wasn't straight or there was a directional error.

➡️ Conclusion: The measured displacement (2.25 m) does not match the calculated displacement (~8 m).

So answer to “Did your measured displacement match?” → No ✔ (correct)

But the student's calculated displacement was written as 792 cm = 7.92 m, which matches our calculation. So that's correct.

And distance = 3.25 + 1.65 + 6.38 = 11.28 m → rounded to 11 m

✔ So corrections:
- Distance: 11 m
- Calculated displacement: 7.92 m → 8 m
- Measured displacement: 2.25 m → likely incorrect due to measurement error

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## ✔ Activity #2

Now, this one involves directions: North, West, South, East.

Given:

1. North: 10 steps → 312 cm = 3.12 m → 3 m
2. West: 15 steps → 484 cm = 4.84 m → 5 m
3. South: 10 steps → 306 cm = 3.06 m → 3 m
4. East: 20 steps → 685 cm = 6.85 m → 7 m

Step 5: Measured displacement from origin: 200 cm = 2 m

Step 6: Calculate total distance:

Add all segments:
- North: 3 m
- West: 5 m
- South: 3 m
- East: 7 m

→ Total distance = 3 + 5 + 3 + 7 = 18 m

But the student wrote Distance = 207 → probably meant 207 cm = 2.07 m, which is wrong.

✘ Error here — they may have added centimeters incorrectly.

Let’s check:
- 312 + 484 + 306 + 685 = ?

Calculate:
- 312 + 484 = 796
- 796 + 306 = 1102
- 1102 + 685 = 1787 cm = 17.87 m → rounded to 18 m

✔ So Distance = 18 m

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Now, calculate displacement:

Use vector components.

Let’s define:
- North/South as y-axis (N = +, S = –)
- East/West as x-axis (E = +, W = –)

| Direction | Distance (m) | x-component | y-component |
|----------|---------------|-------------|-------------|
| North | 3 | 0 | +3 |
| West | 5 | –5 | 0 |
| South | 3 | 0 | –3 |
| East | 7 | +7 | 0 |

Now sum:
- Net x = –5 + 7 = +2 m (East)
- Net y = +3 – 3 = 0 m

So displacement = √(x² + y²) = √(2² + 0²) = 2 m East

✔ Measured displacement was 200 cm = 2 m → matches!

So the measured displacement matches the calculated displacement.

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## ✔ Final Answers & Corrections:

🟩 Activity #1 Summary

- Distance walked:
325 cm + 165 cm + 638 cm = 1128 cm = 11.28 m → 11 m ✔
→ Student had 1.128 cm → ✘ Wrong units! Should be 11 m

- Calculated displacement:
Forward: 3.25 + 6.38 = 9.63 m
Backward: 1.65 m
Net: 9.63 – 1.65 = 7.98 m → 8 m
→ Student wrote 792 cm = 7.92 m → close enough, acceptable

- Measured displacement: 225 cm = 2.25 m → ✘ Does NOT match (should be ~8 m)

- Did it match? → No ✔ (Correct)

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🟩 Activity #2 Summary

- Distance:
312 + 484 + 306 + 685 = 1787 cm = 17.87 m → 18 m
→ Student wrote 207 → ✘ Incorrect
Likely meant 1787 cm or 18 m

- Measured displacement: 200 cm = 2 m → ✔ Correct

- Calculated displacement:
Net x = –5 + 7 = +2 m
Net y = +3 – 3 = 0 m
→ Displacement = 2 m East → matches measured value ✔

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## ✔ Final Answer Box

Activity #1

- Distance: 11 m
- Calculated displacement: 8 m
- Measured displacement: 2.25 m
- Match? No

Activity #2

- Distance: 18 m
- Measured displacement: 2 m
- Calculated displacement: 2 m east
- Match? Yes

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## ✔ Explanation of Key Concepts

- Distance is scalar (only magnitude): total path length.
- Displacement is vector (magnitude + direction): straight line from start to finish.

In Activity #1, you moved forward, then back, then forward again — so net displacement is forward, not zero.

In Activity #2, you went North, West, South, East — and ended up 2 m east of origin because:
- North and South canceled (3 m vs 3 m)
- West and East: 5 m west, 7 m east → net 2 m east

That’s why displacement is 2 m east.

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## ✔ Conclusion

The student made two major errors:
1. Units confusion: Wrote "1.128 cm" instead of 11.28 m
2. Misread distance: Wrote "207" instead of 1787 cm → 18 m

With corrected calculations:
- Activity #1: Distance = 11 m, Displacement = 8 m (measured 2.25 m → mismatch)
- Activity #2: Distance = 18 m, Displacement = 2 m (matches measured)

✔ These results make sense physically.

Let me know if you'd like a diagram or visual explanation!