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Introduction

Distance and displacement are two quantities that seem to mean the same but are distinctly different with different meanings and definitions. 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.”

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.

Distance and Displacement - Motion, Class 9, Science

Distance = Length of the path I (ACB)                            
Distance is a scalar quantity.

Unit In SI system: metre (m)
In CGS system: centimeter (cm)
Large unit Kilometre (km)
Distance Formula: Distance and Displacement - Motion, Class 9, Science 

Displacement

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 of an object = Final position – Initial position of the object.
Distance and Displacement - Motion, Class 9, ScienceDisplacement at point A = 0
Distance travelled at point A = 0
Displacement = Δx = x− x0
xf = Final Position
x0 = Initial Position
Δx = Displacement

Examples of Distance and Displacement

Q.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?
Ans:
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

Q.2. An object moves along the grid through points A, B, C, D, E, and F as shown below. The side of square tiles measures 0.5 km.
(a) Calculate the distance covered by the moving object.
(b) Find the magnitude of the displacement of the object.

Distance and Displacement - Motion, Class 9, ScienceAns: (a) The distance covered by the moving object is calculated as follows:
AB + BC + CD + DE + EF
3 + 1 + 1.5 + 0.5 + 0.5 = 6.5 km
The distance covered by the moving object is 6.5 km.
(b) The initial point is A and the final point is F, hence the magnitude of the displacement is equal to the distance AF which is calculated by applying Pythagoras’s theorem to the triangle AHF as shown in the figure below:
Distance and Displacement - Motion, Class 9, ScienceApplying the Pythagorean formula, we get
Distance and Displacement - Motion, Class 9, Science
Substituting the formula, we get
Distance and Displacement - Motion, Class 9, Science
The magnitude of displacement is 2.5 km.

Distance vs Displacement

Distance and Displacement - Motion, Class 9, Science


Go through Short Notes of the chapter Motion from here.

Go through NCERT solutions of the chapter Motion from here. 

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FAQs on Distance and Displacement - Motion, Class 9, Science

1. What is the difference between distance and displacement?
Ans. Distance refers to the total length covered by a moving object regardless of direction and path. Displacement, on the other hand, refers to the shortest distance between the initial and final position of an object. Distance is a scalar quantity while displacement is a vector quantity.
2. How do you calculate displacement?
Ans. To calculate displacement, subtract the initial position of an object from its final position. Displacement is a vector quantity, so it has both magnitude and direction. Thus, displacement is represented as a vector with an arrow pointing from the initial position to the final position.
3. What is the difference between speed and velocity?
Ans. Speed is the rate at which an object covers distance, while velocity is the rate at which an object changes its displacement. Speed is a scalar quantity, while velocity is a vector quantity. The speed of an object can be calculated by dividing the distance covered by the time taken, while velocity can be calculated by dividing the displacement by the time taken.
4. Can the displacement be greater than the distance?
Ans. No, the displacement of an object can never be greater than the distance it has covered. Displacement is the shortest distance between the initial and final positions of an object, while distance is the total length covered by the object. Since the shortest distance can never be greater than the total distance, the displacement can never be greater than the distance.
5. How can you determine the direction of velocity?
Ans. The direction of velocity is determined by the direction of displacement. Velocity is a vector quantity, so it has both magnitude and direction. The direction of velocity is the same as the direction of displacement, which is the shortest distance between the initial and final positions of the object. The direction of velocity can be represented by an arrow pointing in the direction of displacement.
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