Overview
This lecture introduces motion in one dimension, focusing on defining position, displacement, average velocity, and average speed, with worked examples to clarify differences between these core concepts.
Treating an Object as a Particle
- Objects in motion are often simplified as particles in physics, ignoring irrelevant details such as rotation.
- Treating something as a particle means focusing only on translational motion and ignoring other degrees of freedom.
Position and Displacement
- Position refers to the location of an object at a given time, often denoted as ( x ) in a chosen coordinate system.
- Displacement (( \Delta x )) is the change in position: ( x_{final} - x_{initial} ).
- Displacement is a vector; its sign (positive or negative) indicates direction along the chosen axis.
Average Velocity
- Average velocity is defined as displacement divided by the time interval: ( \bar{v} = \frac{\Delta x}{\Delta t} ).
- The sign of average velocity depends on the direction of displacement.
- On a position vs. time (x-t) graph, average velocity corresponds to the slope of the line between two points.
Average Speed
- Average speed is total distance traveled divided by total time: ( \bar{v}_{s} = \frac{\text{total distance}}{\Delta t} ).
- Unlike velocity, average speed is always positive (or zero) since distance cannot be negative.
Worked Example: Round-Trip Motion
- A person travels from A to B at speed ( V_1 ), returns from B to A at speed ( V_2 ).
- Average velocity for the entire trip is zero since initial and final positions are the same.
- Average speed is ( \frac{2L}{\frac{L}{V_1} + \frac{L}{V_2}} = \frac{2 V_1 V_2}{V_1 + V_2} ) (after canceling L).
Key Terms & Definitions
- Particle β An object treated as a point, ignoring internal structure or rotation.
- Position (( x )) β Location of an object on a coordinate axis.
- Displacement (( \Delta x )) β Change in position; a vector.
- Average velocity (( \bar{v} )) β Displacement divided by time interval.
- Average speed (( \bar{v}_s )) β Total distance divided by total time.
Action Items / Next Steps
- Read Section 2.1 in the textbook (10th edition).
- Attempt Homework 1, including the round-trip speed/velocity problem.
- Review x-t graphs and practice identifying slopes as average velocities.