Distance and Displacement

Distance and Displacement are two crucial terms of Mechanics that may seem the same but have different meanings and definitions. Distance is a measure of “How much path is covered by an object in motion?” While Displacement is the measure of “How much path is covered by the object in a particular direction?” Hence, the major difference between distance and displacement is that distance is a scalar quantity and displacement is a vector quantity. 

Despite this difference, both quantities have some similarities also. The unit of distance and displacement is meter (m). Let’s learn more about Distance and Displacement in this article by understanding some important concepts like, What is Distance, Distance formula, What is Displacement, Displacement formula, Differences, Similarities, and Examples of Distance and Displacement.

What is Distance?

Distance is the total path covered by the object in motion, irrespective of the direction of the path. Distance is known as a scalar quantity as only the path length covered is measured and the direction of motion is not considered. The distance can never be zero or negative, it is only be positive. 

Distance gives detailed information about the entire path covered during motion. Distance is represented as ‘d’ and it is not represented with an arrow as the direction is not involved. 

Distance Formula

Mathematically, Distance can be defined as:

Distance = Total length of the Path covered from one point to another / Total Time Taken

Since we know that,

Speed = Distance / Time 

Therefore,

Distance = Speed × Time

or

d = s × t

where,

d is the distance covered by an object,

s is the Speed, and 

t is the Time Taken.

What is Displacement?

Displacement is defined as the total change in the position of the object along with the direction of motion. Displacement is known to be vector quantity as along with the magnitude of the changed position, the direction of the motion is also taken into account. Displacement can be positive, negative, or zero.

Displacement does not give detailed information on the entire path length, the initial and the final position is required for the calculation of the displacement. Displacement is represented as ‘S’ and an arrow is used to indicate that displacement is a vector quantity. Displacement always has a straight-lined path as the initial and final points are directly connected to find the displacement.

Displacement Formula

Mathematically, the displacement is defined as,

∆x = x_f – x₀

where,

x_f is the final position of the object, 

x₀ is the starting position of the object, and

∆x is the displacement of the object.

Difference Between Distance and Displacement

Here are the tabular representation of the differences between Distance and Displacement:

Distance	Displacement
Distance is the total path covered by the object in motion, irrespective of the direction of the path.	Displacement is defined as the total change in the position of the object along with the direction of motion.
Distance is denoted by the symbol d.	Displacement is represented by the letter s.
Distance is a Scalar Quantity.	Displacement is a Vector Quantity.
When Distance is calculated, only the length of the path is considered, ignoring its direction.	When Displacement is calculated, both the length of the path and the direction of the object are considered.
The formula to calculate the distance (d) is equal to Speed × time.	The formula to calculate the Displacement (s) is equal to Velocity × time.
The distance can only have positive values.	However, displacement can have positive, negative, or zero.

Similarities Between Distance and Displacement

Despite a number of differences between them, both distance and displacement have quite similarities as well, some of them are listed below:

• The SI unit of both the Physical quantity is meter (m) only.
• Both distance and displacement require initial and final points for measurement.
• When the direction is not considered both are equal in magnitude, in most cases.
• Both have the same dimensions formula.

Solved Examples on Distance and Displacement

Example 1: What is the distance and displacement from the given figure,

Solution:

Distance is the total path length,

Distance = (3+ 4) m = 7meters.

Displacement is the direct line from A to B,

Displacement= 

Therefore, Displacement= 5 meters (south- east direction).

Example 2: A particle has covered a distance of 1000 meters and a displacement of 200 meters in 1 min 40 sec. Find the Speed and Velocity of the particle during motion.

Solution:

Time taken = 1 minute 40 seconds = 100 seconds

Speed= distance/ time

Speed= 1000/ 100 = 10m/sec

Velocity= displacement/ time

Velocity= 200/100 = 2 m/sec

Example 3: The speed and the velocity of a car are given as 5 m/sec, and the time taken in the whole journey is 5 minutes, what are the observations drawn from that information?

Solution:

Time taken in the whole journey= 5 minutes= 5× 60= 300 seconds.

Speed given= 5 m/sec

Distance= 5× 300= 1500 meters= 1.5 km

Velocity= 5 m/sec

Displacement= 5× 300= 1500 meters= 1.5 km.

Observation- The distance and the displacement are both equal since the speed and the velocity of the car is equal. Therefore, it can be said that the car has traveled only in a straight direction.

Example 4: A boy decided to take a walk around his town in the evening, he started from his home and traveled approximately 1500 meters in 30 minutes. He finally came back to his home. Find the values of the following quantities,

• Speed
• Displacement
• Velocity

Solution:

Given: Distance= 1500 meters, Time= 30 minutes= 30× 60 seconds= 1800 seconds.

Speed = distance/ time

Speed= 1500/1800= 0.833 m/sec

Displacement= 0 meters (as the boy finally came back to his house, so the initial and the final point coincided).

Velocity = Displacement/ time= 0/ 1800= 0 m/sec

FAQs on Distance and Displacement

Question 1: List out at least 3 differences between distance and displacement.

Answer:

Difference between distance and displacement,

Distance	Displacement
Distance is the total path length	It is the length between initial and final points.
Distance has no direction	Displacement has direction
Distance gives detailed info about path length	Displacement does not give detailed information about the path length.

Question 2: Is this possible to have a negative distance?

Answer:

No, distance can never be negative. Distance is always positive. However, displacement can be negative.

Question 3: Can displacement be zero?

Answer:

Yes, displacement can be zero.

Question 4: When do the Distance and Magnitude of Displacement become equal?

Answer:

The distance and the magnitude become equal when the motion is in a fixed direction or in one direction.

Question 5: Write any two differences between distance and displacement.

Answer:

Distance is a scalar quantity while displacement is a vector quantity. 

Also, Displacement can be positive, negative or zero but Distance can only be positive.