**Distance and Displacement are Scalar and Vector Quantities, respectively.**

A **vector **quantity has a direction and a magnitude, while a **scalar **has only a magnitude. You can tell if a quantity is a **vector **by whether it has a direction associated with it.

Simply put, Distance measures the arbitrary length between two points, whereas Displacement measures the arbitrary length and the direction from point A to B.

**Example:** If a person goes 10 m to the East and then 10 m to the North, followed by 10 m West and then finally 10 m South, the person will be back to where he is, correct? In this scenario he would have traveled 40 m, whereas his displacement from the starting point would be zero.

In order to calculate displacement, simply measure the distance from the initial point to the final point and then write the direction. If the final position is not in line with the compass directions (perhaps the solution direction seems North East, write in two directions such as x m East, y m North.

Equation for displacement = X_{f} – X_{i}

X_{f} = final position

X_{i} = initial position

Displacement and distance will come in handy when utilizing kinematics (the movement of objects). Usually upward movement has positive displacement (x) and downward movement has negative displacement (-x). Distance is commonly termed as d. Displacement is commonly termed as x.

## Practice problems:

1. Chanice drives her scooter 7 meters north. She stops for lunch and then drives 5 meters east. What distance did she cover? What was her displacement?

The total distance, or the length of travel along the path taken = 5 + 7 = 12 m.

Use the distance formula to find the displacement, or the straight-line length between the final and initial position:

2. Alex goes cruising on his dirt bike. He rides 700 m north, 300 m east, 400 m north, 600 m west, 1200 m south 300 m east and finally 100 m north. What distance did he cover? What was his displacement?

The total distance, or the length of travel along the path taken = 700 + 300 + 400 + 600 + 1200 + 300 + 100 = 3600

To find the displacement, plot the points of the path traveled to determine the final and initial position. Using his starting point as the origin,

Looking at the diagram above, Alex finished where he started, so his displacement is zero.

3. On his fishing trip Justin rides in a boat 12 km south. The fish aren’t biting so they go 4 km west. They then follow a school of fish 1 km north. What distance did they cover? What was their displacement?

Distance = 12 + 4 + 1 = 17 km

To find displacement, the first thing is to plot the points along the path of travel. Using his starting position as the origin.

The initial position is (0,0), and the final position is (-4, -11)

To find displacement, use the distance formula:

**Reference:**

https://www.physicsclassroom.com/class/1DKin/Lesson-1/Distance-and-Displacement