# Distance and Displacement

## Introduction

Distance and displacement are two quantities that may seem to mean the same thing yet have distinctly different definitions and meanings.
- Distance is a scalar quantity that refers to "how much ground an object has covered" during its motion.
- Displacement is a vector quantity that refers to "how far out of place an object is" it is the object's overall change in position.

Let's consider the motion of a physics instructor who walked 4 meters East, 2 meters South, 4 meters West, and finally 2 meters North. See illustration below:

Even though the physics instructor walked a total distance of 12 meters, his displacement is 0 meters.

Displacement, being a vector quantity, must give attention to direction.

Distance is different from Displacement:

- Distance is Scalar quantity. Displacement is Vector quantity.
- Distance is how much ground an object has covered during its motion.
- Displacement is the overall change in object position.

### Exercises: Distance and Displacement

#### Exercise 1

Adam drove off his car 1 mile North, 3 miles West, 1 mile South, and finally 3 miles km East.

Question: What is the total distance from the starting point? What is the total displacement from the starting point?

Answers:

**
Total distance from the starting point = 8 miles.**

Total displacement from the starting point = 0 miles.

#### Exercise 2

Questions: What is the displacement of Lisa if she begins at Harvard Square, runs for 1.5 miles to Harvard Medical School and then returns back to Harvard Square?

What is the total distance?

Answers:

**
Total distance from the starting point = 3 miles.**

Total displacement from the starting point = 0 miles.

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Date of last modification: Summer , 2019