Suggested languages for you:

Americas

Europe

Q1CQ

Expert-verified
Found in: Page 78

### College Physics (Urone)

Book edition 1st Edition
Author(s) Paul Peter Urone
Pages 1272 pages
ISBN 9781938168000

# Give an example in which there are clear distinctions among distance traveled, displacement, and magnitude of displacement. Specifically, identify each quantity in your example

Distance is a scalar quantity, and displacement is a vector quantity. Distance needs only magnitude to be mentioned, whereas displacement needs magnitude.

See the step by step solution

## Step 1: Distance and Displacement

Distance: The total number of lengths covered by any object in terms of number is considered as the distance covered by that object.

The distance covered by the objects is measured in many units like kilometers, meters, etc.

But the SI unit of distance is METER.

To mention the value of distance, we only need the magnitude. In which direction the body is moving is not necessary.

Hence distance is said as a scalar quantity.

Displacement: The displacement is the length that is measured between the intial position of the body and the final position of the body. The length measured is the shortest length.

To describe displacement, we need both magnitudes as well as direction.

## Step 2: Example of distance and displacement

Suppose a man is walking in a park shaped like a square. The side of the park is ${\mathbf{10}}{\text{}}{\mathbf{meters}}$. He takes 2 rounds and comes back to the intial position, as shown in the figure.

So, in this case, let's find out the distance.

Distance traveled by the man is the perimeter of the square,

$\begin{array}{l}=\mathbf{4}\mathbf{a}\\ =\mathbf{4}\text{}\mathbf{x}\text{}\mathbf{10}\\ =\mathbf{40}\text{}\mathbf{meter}\end{array}$

He takes two rounds, so the total distance traveled by the man will be,

$\begin{array}{l}=\mathbf{40}+\text{}\mathbf{40}\\ =\mathbf{80}\text{\hspace{0.17em}}\mathbf{m}\end{array}$

To find out displacement, we need to calculate the shortest distance between the intial and the final position.

Here, in this case, the intial and final positions are the same so that the shortest distance will be zero.

Therefore displacement is a vector quantity, while distance is a scalar quantity. The magnitude of a distance must be specified, whereas the magnitude of a displacement must be mentioned.