Distance vs. Displacement

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Distance

Distance: How Much Ground You Covered

Definition: Distance is the total length of the path you travel.

Key Trait: It’s a scalar quantity, which means it only tells you how much you moved, not where or in what direction.

Example: If you walk 3 meters forward and then 2 meters back, your total distance is 5 meters.��3 m + 2 m = 5 meters

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Displacement

Displacement: How Far You Are From Where You Started

Definition: Displacement is the straight-line change in position from your starting point to your ending point.

Key Trait: It’s a vector quantity, which means it includes both magnitude (how far) and direction.

Example: Using the same walk. 3 meters forward, then 2 meters back, your displacement is: ��3 m - 2 m = 1 meter forward

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Quick Analogy: The Pizza Delivery Route�

Imagine a pizza delivery person drives 10 blocks in a zigzag to reach a house that’s only 6 blocks away in a straight line.

Distance = 10 blocks (the actual path driven)

Displacement = 6 blocks (straight from the restaurant to the house)��

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Math Example #1: Distance & Displacement

A lion spots a baby zebra and sprints to the right. After the lion ran 45 meters, he gets sad about eating a zebra and decides to head back moving 20 meters to the left.

1. What distance did the lion travel?
2. What displacement did the lion travel?

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65 m

25 m or 25m to the right

Conceptual Example #5: Distance & Displacement

The Odometer in your car, does it track the distance your car has traveled or does is track the displacement of your car? Explain.

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Odometer

Distance. If you went east, west, south, or in any direction it would just record how much the car moved regardless of direction.

Math Example #2: Distance & Displacement

Jim travels 60 meters East to go to Cindy's house. However, Cindy is not home so he decides to head 40 meters West to hang out with Harry. 

1. What distance did Jim travel? 
2. What is Jim's displacement?

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100 meters

20 meters (the positive number implies east)

Or 20 meters east

Harry's House

Cindy's House

Jim

Math Example #3: Distance & Displacement

Cindy notices Jim coming to her house and decides to run out the door 150 meters to the East. Afterward, Cindy goes to Harry's house which is 40 meters to the west of Cindy's house. 

1. What distance did Cindy travel? 
2. What is Cindy's displacement? 

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340 meters

-40 meter or 40 meters West

Harry's House

Cindy's House

Cindy

Math Example #4: Distance & Displacement

Jim’s mom tells Jim to go buy some eggs at the grocery. On his way Jim sees and walks up to a RED PENGUIN 50 meters to the right of the grocery store. He’s so excited he forgets about the eggs and runs to Cindy’s house to tell her about this. Then Jim gets a call from his mom asking about the eggs. He rushes to the grocery store before it closes, but as soon as he gets there he passes out. 

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1. What is Jim’s displacement?
2. What is x?
3. What is total distance Jim traveled?
4. How far does Cindy live from Jim?

200 m

75 m

450 m

125 m

200 m

50 m

125 m

x

Jim's House

Cindy's House

Grocery

Conceptual Example #6: Distance and Displacement

1. Can you drive your car in such a way that the distance it covers is greater than the magnitude of its displacement? 
2. Can you drive your car in such a way that the distance it covers is equal to the magnitude of its displacement?
3. Can you drive your car in such a way that the distance it covers is less than the magnitude of its displacement?

If your answer is yes, give an example for each case. If your answer is no, explain why for each case.

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1. Yes, if you do not drive in a straight line
2. Yes, if you drive in a straight line
3. No