Distance and Displacement: Definition, Formula, Differences and Solved Examples

Distance and displacement are two important concepts that help us describe the motion of objects. Suppose you walk around your school playground and return to the gate where you started. The path you covered is large, but your change in position is zero. That's where displacement becomes important. 

Distance tells us the total path covered by an object, while displacement gives the shortest straight-line distance between the starting and ending points along with its direction. This article gives a detailed explanation of what is distance and displacement, how to calculate distance and displacement, the differences, and examples.

Table of Contents

• Understanding What is Distance and Its Formula
• Understanding What is Displacement and Its Formula
• Difference Between Distance and Displacement
• Key Similarities Between Distance and Displacement
• Solved Examples on Distance and Displacement

Understanding What is Distance and Its Formula

Distance is the total length of the path covered by an object during its motion. It does not depend on the direction in which the object moves.

In simple words, 

“Distance tells us how much path an object has travelled from one place to another.”

For better understanding, imagine that Riya walks 6 m towards the library and then walks another 4 m towards the playground. 

The total path covered by Riya is, 

Distance = 6 m + 4 m = 10 m

So, the distance travelled by Riya is 10 m.

Interestingly! Even if Riya changes direction while walking, the distance is always the total path covered during her journey.

But, how do we find the distance travelled by an object? Let's discuss in detail.

Mathematical Formula to calculate the Distance 

When we know the speed of an object and the time it has been moving, we can easily calculate the distance covered.

We know that, 

Speed = Distance ÷ Time

By rearranging this formula, we get:

Distance = Speed × Time

Or simply,

d = s × t

Where d is the distance travelled by the object, s is the speed of the object, and t is the time taken.

Important Points to Remember About Distance

Distance is a scalar quantity. It has only magnitude and no direction. Distance is always positive. Its SI unit is meter (m). It depends on the actual path travelled by the object.

Understanding What is Displacement and Its Formula

Displacement is nothing but the shortest straight-line distance between the starting point and the ending point of an object's motion. It also tells us the direction in which the object has moved.

In simple words, 

“Displacement shows how far and in which direction an object is from its starting position.”

Unlike distance, displacement does not depend on the actual path taken by the object. It only considers the initial and final positions.

Now you may ask, how do we calculate the displacement of an object?

Mathematical Formula to calculate the Displacement

Since displacement tells us the change in the position of an object, we only need to know its starting position and final position.

The formula for displacement is,

Δx = xf - xi

Where, Δx is the displacement of the object, xf is the final position of the object, and xi is the initial position of the object

In simple words,

Displacement = Final Position - Initial Position

The fact is that this formula gives the shortest straight-line distance between the starting and ending points, along with its direction.

Important Points to Remember About Displacement

Displacement is a vector quantity. It has both magnitude and direction. Displacement can be positive, negative, or zero. Its SI unit is meter (m).

Differences between Distance and Displacement

Distance and displacement may sound similar, but they have different meanings in physics. Distance tells us the total path covered by an object, while displacement tells us the shortest straight-line distance between the starting and ending points, along with the direction of motion.

The table below shows the major differences between distance and displacement.

Distance	Displacement
Distance is the total length of the path travelled by an object.	Displacement is the shortest straight-line distance between the initial and final positions of an object.
It does not depend on the direction of motion.	It always includes the direction of motion.
Distance is a scalar quantity.	Displacement is a vector quantity.
Only the magnitude of the path is considered while calculating distance.	Both magnitude and direction are considered while calculating displacement.
Distance is always positive.	Displacement can be positive, negative, or zero.
Distance depends on the actual path followed by the object.	Displacement depends only on the starting and ending positions.
The value of distance is always greater than or equal to displacement.	The magnitude of displacement is always less than or equal to distance.

Key Similarities Between Distance and Displacement

Even though distance and displacement are different concepts, they also have a few things in common. Let's try to understand their similarities.

• Same SI Unit:Both distance and displacement are measured in meters (m).
• Used to Describe Motion: Both quantities help us explain how an object moves from one place to another.
• Depend on Position: To measure either quantity, we need to know the object's starting and ending positions.
• Can Have the Same Value:If an object moves in a straight line without changing its direction, the distance and displacement become equal.
• Same Dimensional Formula:Both have the same dimensional formula:
  [M⁰L¹T⁰]
• Both Measure Length: Distance and displacement are used to measure the length associated with the motion of an object.

Solved Examples of Distance and Displacement

Numerical 1: Priya travels 180 km north to visit her grandparents. Later, she travels 70 km south to meet her cousin. 

Find Priya's total displacement.

Solution:

Here, the initial position, xi = 0 km

Final position,

xf = 180 km north - 70 km south

xf = 110 km north

Using the displacement formula,

Δx = xf - xi

Δx = 110 km - 0

Δx = 110 km north

The total displacement of Priya is 110 km north.

Interestingly! Although Priya travelled a total distance of 250 km (180 km + 70 km), her displacement is only 110 km north because displacement depends only on the starting and ending positions.

Numerical 2: A circular park has a radius of 3 m. Rohan rides his bicycle three complete rounds around the park and stops at the point where he started.

Find:

• The total distance travelled by Rohan.

• The displacement of Rohan.

Solution:

Given, Radius of the park, r = 3 m

Circumference of the park:

C = 2πr

C = 2 × 3.14 × 3

C = 18.84 m

Since Rohan completes three rounds,

Distance travelled = 3 × 18.84

Distance travelled = 56.52 m

Now, let's calculate the displacement.

Since Rohan finishes at the same point where he started, his initial and final positions are the same.

Displacement = 0 m

Distance travelled = 56.52 m

Displacement = 0 m

Interestingly! Even though Rohan travelled 56.52 m, his displacement is 0 m because he returned to his starting point.

In this article, we have learned that distance and displacement are two important concepts used to describe the motion of an object. Distance tells us the total path covered during motion, while displacement gives the shortest straight-line distance between the starting and ending points, along with direction.