Distance and Displacement in detail explanation

 Displacement and distance are fundamental concepts in physics, especially in the study of motion. While they are often confused, they represent different quantities.

Distance

Definition: Distance is a scalar quantity that represents the total length of the path traveled by an object, regardless of the direction.

Characteristics:

• Always positive or zero.
• Does not consider the direction of motion.
• Only the magnitude of the path traveled is measured.

Example: Imagine you walk from point A to point B and then to point C.

• If point A to point B is 4 meters, and point B to point C is 3 meters, the total distance traveled is 4 + 3 = 7 meters.
• Even if you walked in a curved path, the distance would still be the total length of the path you covered.

Displacement

Definition: Displacement is a vector quantity that represents the change in position of an object. It has both magnitude and direction.

Characteristics:

• Can be positive, negative, or zero.
• Considers the initial and final position, not the path taken.
• Includes both magnitude and direction (e.g., 5 meters east).

Example: Using the same points A, B, and C:

• If point A is at (0, 0), point B at (4, 0), and point C at (4, 3), the displacement from A to C can be found using the coordinates.
• From A to B, displacement is 4 meters east.
• From B to C, displacement is 3 meters north.
• The total displacement from A to C can be found using the Pythagorean theorem: $\sqrt{4^2+3^2}=\sqrt{16+9}=\sqrt{25}=5$ meters in the northeast direction.

Detailed Comparison with Examples

1. Straight Line Path:

   • Example: You walk 10 meters east.
     • Distance: 10 meters.
     • Displacement: 10 meters east.

2. Round Trip:

   • Example: You walk 5 meters east and then 5 meters west.
     • Distance: 5 + 5 = 10 meters.
     • Displacement: 0 meters (because you end up at the starting point).

3. Rectangular Path:

   • Example: You walk 3 meters north and then 4 meters east.
     • Distance: 3 + 4 = 7 meters.
     • Displacement: $\sqrt{3^2+4^2}=5$ meters (northeast).

Visual Representation

Consider a coordinate plane:

• Path Taken (Distance):

  • From point (0,0) to (4,0): 4 meters.
  • From (4,0) to (4,3): 3 meters.
  • Total distance: 4 + 3 = 7 meters.

• Direct Path (Displacement):

  • From point (0,0) to (4,3).
  • Using the coordinates, the displacement is $\sqrt{4^2+3^2}=5$ meters northeast.

Conclusion

• Distance is the total ground covered without considering the direction.
• Displacement is the straight-line distance from the starting point to the ending point, considering the direction.

Understanding these differences is crucial in physics as it helps describe motion accurately. While distance tells us how much ground an object has covered, displacement tells us how far out of place an object is from its initial position.