Distance
* Definition: The total length of the path traveled.
* In a circle: If the body completes a full circle, the distance traveled is the circumference of the circle: Distance = 2πr (where 'r' is the radius).
* Partial circle: If the body travels only part of the circle, the distance is the length of that arc. This can be calculated using the formula: Distance = (θ/360°) * 2πr (where 'θ' is the angle of the arc in degrees).
Displacement
* Definition: The straight-line distance between the starting point and the ending point.
* In a circle:
* If the body completes a full circle, its displacement is zero because it ends up back where it started.
* If the body travels part of the circle, its displacement is the chord connecting the starting and ending points. The magnitude of this displacement can be calculated using the law of cosines.
Key Differences
* Distance: A scalar quantity (only magnitude).
* Displacement: A vector quantity (both magnitude and direction).
Example
Imagine a car driving in a circular track with a radius of 10 meters.
* If the car completes one full lap:
* Distance = 2π(10) = 20π meters
* Displacement = 0 meters (it ends up back where it started).
* If the car drives a quarter of the track:
* Distance = (90°/360°) * 2π(10) = 5π meters
* Displacement would be the length of the diagonal across the quarter circle (which can be calculated using the law of cosines).
Let me know if you have any other questions!
