Lecture Notes: Motion in a Straight Line

Key Concepts

• Motion in a Straight Line: Understanding the basic fundamentals of motion, specifically distance and displacement.

Distance vs. Displacement

Distance

• Definition: Total length of the path traveled.
• Unit: Meter (m), which is an SI unit.
• Nature: Scalar quantity (only magnitude, no direction).
• Properties:
  • Cannot be negative.
  • Can be zero or positive.

Displacement

• Definition: Change in the position of the object (shortest distance between the starting and ending points).
• Formula: Displacement ( \Delta x = x_f - x_0 )
  • ( x_f ): Final position
  • ( x_0 ): Initial position
• Nature: Vector quantity (has both magnitude and direction).
• Properties:
  • Can be positive, negative, or zero.

Examples

Example 1: Circular Path

• Scenario: Moving in a semicircle from point A to B.
• Distance Calculation:
  • Path traveled is the semicircle.
  • ( \text{Distance} = \frac{2\pi R}{2} = \pi R )
  • Given radius ( R = 5 ) meters, ( \pi R = 15.7 ) meters.
• Displacement Calculation:
  • Straight line from A to B (diameter of the circle).
  • Displacement = Diameter = ( 2 \times 5 = 10 ) meters.

Example 2: Zigzag Path

• Scenario: Object moves in a zigzag pattern.
• Distance Calculation: Sum of all path segments (e.g., 2m + 3m + 2m + 3m + 2m = 12m).
• Displacement Calculation:
  • Connects starting point to endpoint in a straight line.
  • Example total displacement: 6 meters.

Example 3: Right Angle Triangle Path

• Scenario: Object moves in a right-angle triangle.
• Distance Calculation: Sum of all path segments (e.g., 3m + 4m = 7m).
• Displacement Calculation:
  • Calculated using Pythagorean theorem: ( \sqrt{3^2 + 4^2} = 5 ) meters.
  • Angle calculation: ( \theta = \tan^{-1}(\frac{4}{3}) = 53.13^\circ ).

Example 4: Closed Loop

• Scenario: Object moves in a complete circle.
• Distance Calculation: Circumference of the circle ( 2\pi R ).
  • Given radius ( R = 10 ) meters, total distance = 62.8 meters.
• Displacement: Zero, as starting and ending points are the same.

Conclusion

• Distance is always greater than or equal to displacement.
• Displacement can be positive, negative, or zero, emphasizing its vector nature.
• Distance is a scalar quantity, hence always non-negative.

This lecture aimed to clarify the distinction between distance and displacement through definitions, properties, and examples.