 # Distance And Displacement

Distance and displacement are two quantities that seem to mean the same but are distinctly different with different meanings and definition. Distance is the measure of “how much ground an object has covered” during its motion while displacement refers to the measure of how far out of place is an object. In this article, let us understand the difference between distance and displacement.

## What is Distance?

Distance is the total movement of an object without any regard to direction. We can define distance as to how much ground an object has covered despite its starting or ending point.

Let’s understand with the following diagram Distance here will be = 4m + 3m + 5m = 12 m

### Distance Formula

$\Delta d =d_{1} + d_{2}$

## How is Displacement defined?

Displacement is defined as the change in position of an object. It is a vector quantity and has a direction and magnitude. It is represented as an arrow that points from the starting position to the final position. For Example- If an object moves from A position to B, then the object’s position changes. This change in position of an object is known as Displacement. Displacement = $\Delta x = x_{f}- x_{0}$

$x_{f}$ = Final Position

$x_{0}$ = Initial Position

$\Delta x$ = Displacement

## Examples of Distance And Displacement

Question 1.  John travels 250 miles to North but then back-tracks to South for 105 miles to pick up a friend. What is John’s total displacement?

Answer: John’s starting position  Xi= 0.

Her final position Xf is the distance travelled N minus the distance South.

Calculating displacement, i.e.D.

D = ΔX = (Xf – Xi)

D = (250 mi N – 105 mi S) – 0

D = 145 mi N

Question 2. Julia throws the ball 30 feet North for your dog. The dog catches the ball and takes it past Julia to her brother, who is standing 5 feet to the South of where she is. Calculate the total displacement of the ball?

Answer: Julia’s initial position with the ball ( Xi) = 0.

As displacement is a vector quantity, ‘direction’ is considered. Xf = (30 feet S – 25 feet N),

so, Xf = -5 feet S.

D = ΔX = (Xf – Xi)

D = (30 ft S – 25 ft S) – 0

D = 5 ft S of Julia’s starting position 