Overview
This lecture introduces one-dimensional kinematics, focusing on the concepts of scalars and vectors, and provides key formulas for calculating displacement, speed, velocity, and acceleration.
Scalars vs. Vectors
- Scalar quantities have magnitude only (e.g., mass, distance, speed, temperature).
- Vector quantities have both magnitude and direction (e.g., displacement, velocity, acceleration).
- Displacement is distance with a specified direction; displacement = final position - initial position.
- Speed describes how fast something moves (scalar); velocity is speed with direction (vector).
- Temperature is scalar: has magnitude only, direction is not applicable.
Distance, Displacement, Speed, and Velocity
- Distance is always positive (scalar); displacement can be positive or negative (vector).
- Displacement equals the net change in position, considering direction.
- Speed (s) is instantaneous; average speed ((\bar{s})) = total distance / time.
- Average velocity ((\bar{v})) = displacement / time; can be negative or positive.
- Instantaneous speed = |instantaneous velocity|.
Key Formulas and Calculations
- Displacement ((\Delta x)) = (x_{final} - x_{initial}).
- If moving at constant speed: (d = vt), where d is distance/displacement, v is speed/velocity, t is time.
- With constant acceleration:
- Average velocity: (\bar{v} = (v_{initial} + v_{final})/2).
- Displacement: (d = \bar{v} t) or (d = v_{initial}t + 0.5at^2).
- (v_{final} = v_{initial} + at).
- (v_{final}^2 = v_{initial}^2 + 2ad).
- Units must match in calculations (e.g., miles with hours, meters with seconds).
Example Problems
- To solve for time when speed and distance are given, use (d = vt) and convert units as needed.
- Average velocity is based on displacement: (\bar{v} = (x_{final} - x_{initial}) / t).
Key Terms & Definitions
- Scalar — Quantity with magnitude only.
- Vector — Quantity with magnitude and direction.
- Distance — Scalar measure of motion; total path length traveled.
- Displacement — Vector; change in position ((x_{final} - x_{initial})).
- Speed — Scalar; how fast an object moves.
- Velocity — Vector; speed with direction.
- Acceleration — Vector; rate of change of velocity.
- Instantaneous — Value at a specific moment.
- Average — Total change over a time interval.
Action Items / Next Steps
- Write down and memorize the key kinematic formulas.
- Practice converting between units (e.g., meters/sec to miles/hour).
- Solve example problems using given formulas to reinforce concepts.