Grade 7

Intermediate

6 min

Lesson 2 of 12

Distance versus Displacement

Not Started

Discover the difference between the total path traveled and the straight-line change in position.

Imagine you run a full lap around a 400-meter track. Your legs are tired because you ran a long way, but according to physics, your 'change in position' is exactly zero. How can you move so much and end up with nothing to show for it?

Learning Objectives

1.By the end of this lesson, you will be able to differentiate between the total path traveled (distance) and the straight-line change in position (displacement).
2.You'll understand how to calculate displacement in one dimension using the formula $\Delta x = x_{f} - x_{i}$ .
3.You will identify displacement as a vector quantity that requires both magnitude and direction.

Distance: The Total Path

Distance is the total length of the path an object travels. Think of it like the 'odometer' in a car; it only goes up, no matter which way you turn. It is a scalar quantity, meaning it only has a size (magnitude) but no specific direction. If you walk 5 meters East and then 5 meters West, your total distance is $5 + 5 = 10$ meters. You have physically moved 10 meters, regardless of where you ended up.

Quick Check

If a cat chases a laser pointer 3 meters North and then 4 meters South, what is the total distance the cat traveled?

Distance is the total path length; just add the segments together.

Answer

7 meters

Displacement: The Straight-Line Gap

Displacement is the straight-line distance from where you started to where you ended. It is a vector quantity, which means it must include a direction (like North, South, or 'to the right'). We use the symbol

\Delta x

(Delta x) to represent displacement. The formula is:

\Delta x = x_{f} - x_{i}

where

x_{f}

is the final position and

x_{i}

is the starting (initial) position. If you return to your exact starting point, your displacement is always zero!

A robot moves from the 2-meter mark on a ruler to the 10-meter mark. 1. Identify the initial position: $x_{i} = 2$ m. 2. Identify the final position: $x_{f} = 10$ m. 3. Calculate: $\Delta x = 10 - 2 = 8$ meters. 4. Final Answer: $8$ meters to the right.

Quick Check

Why is displacement called a 'vector' while distance is called a 'scalar'?

Think about what extra information you need to get back home.

Answer

Vectors include direction (like North or +), while scalars only show magnitude/size.

Direction Matters

In physics, we often use positive (+) and negative (-) signs to show direction. Usually, moving right or North is positive, while moving left or South is negative. This allows us to calculate displacement even when an object doubles back. If a hiker walks 10 meters East (

+10

) and then 12 meters West (

-12

), their displacement is:

\Delta x = 10 + (-12) = -2\text{ meters}

The negative sign tells us they ended up 2 meters West of where they started.

A swimmer starts at one end of a 50-meter pool ( $x_i = 0$ ), swims to the other end, and then swims 20 meters back toward the start. 1. Total Distance: $50 + 20 = 70$ meters. 2. Final Position ( $x_f$ ): Since they were at 50 and came back 20, they are at the 30-meter mark. 3. Displacement: $\Delta x = 30 - 0 = 30$ meters from the start.

An athlete runs 100m North, 50m South, and then another 50m South. 1. Calculate total distance: $100 + 50 + 50 = 200$ meters. 2. Calculate displacement using signs: $+100$ (North) $- 50$ (South) $- 50$ (South). 3. Result: $100 - 50 - 50 = 0$ meters. 4. Conclusion: Even though the athlete ran 200m, their displacement is 0 because they returned to the start.

Key Takeaways

1Distance is the 'odometer' reading (total path); Displacement is the 'as the crow flies' shortcut.
2Displacement is a vector, so it always needs a direction (e.g., +, -, North, Left).
3The displacement formula is $\Delta x = x_{final} - x_{initial}$ .
4If you end where you started, your displacement is zero, regardless of distance traveled.

Quick Check

Multiple Choice

Which of the following is a vector quantity?

Multiple Choice

A car drives 10 km North and then 10 km South. What is its displacement?

True/False

Distance can be a negative number if you walk backwards.

What's Next?

Review Tomorrow

In 24 hours, try to explain to a friend why a person walking in a circle has a distance of many meters but a displacement of zero.

Practice Activity

Find a tiled floor. Walk 4 tiles forward and 2 tiles back. Calculate your distance and your displacement in 'tiles'.

Browse

Browse

Distance versus Displacement

Learning Objectives

Distance: The Total Path

Displacement: The Straight-Line Gap

Direction Matters

Key Takeaways

Quick Check

What's Next?

Distance versus Displacement

Learning Objectives

Distance: The Total Path

Displacement: The Straight-Line Gap

Direction Matters

Key Takeaways

Quick Check

What's Next?