Overview
This lecture introduces the concepts of speed, velocity, and acceleration, differentiating between scalar and vector quantities and providing calculation methods and examples.
Speed, Velocity, and Acceleration Basics
- Speed is a scalar quantity; it measures how fast something is moving without regard to direction.
- Velocity is a vector quantity; it includes both magnitude (how fast) and direction.
- Acceleration is the change in velocity over time and is also a vector.
Scalars vs. Vectors
- Scalar: Quantity with only magnitude (e.g., speed).
- Vector: Quantity with magnitude and direction (e.g., velocity and acceleration).
- When reporting velocity, always specify direction, or use positive/negative signs in a coordinate system.
Average vs. Instantaneous Velocity
- Average velocity measures total displacement over total time for a trip.
- Instantaneous velocity is the velocity at a specific moment in time.
- In constant motion, average and instantaneous velocities are equal; otherwise, they differ.
Calculating Velocity
- Velocity formula: ( v = \frac{\Delta x}{\Delta t} ), where ( \Delta x ) is change in position and ( \Delta t ) is change in time.
- More generally: ( v = \frac{x_{f} - x_{i}}{t_{f} - t_{i}} ), with ( x_{f} )=final position, ( x_{i} )=initial position, ( t_{f} )=final time, ( t_{i} )=initial time.
- Units for velocity are meters per second (m/s).
Example Problems (Usain Bolt)
- Average velocity for 100m dash in 9.58s: ( v = \frac{100,m}{9.58,s} = 10.4,m/s ).
- First 10 meters in 1.85s: ( v = \frac{10.0,m}{1.85,s} = 5.41,m/s ).
- 60m–70m segment in 0.82s: ( v = \frac{10.0,m}{0.82,s} = 12.2,m/s ).
Acceleration Concepts and Calculation
- Acceleration formula: ( a = \frac{v_{f} - v_{i}}{t_{f} - t_{i}} ).
- Units for acceleration are meters per second squared (m/s²).
- Negative acceleration (deceleration) indicates direction opposite to the chosen positive direction.
Example Problems (Acceleration)
- Acceleration due to gravity: −9.8 m/s² (downward).
- Bugatti Veyron goes from 0 to 60 mph (26.9 m/s) in 2.46 s: ( a = \frac{26.9,m/s}{2.46,s} = 10.9,m/s^2 ).
Key Terms & Definitions
- Speed — Scalar quantity measuring how fast an object moves.
- Velocity — Vector quantity; displacement per time with direction.
- Acceleration — Vector quantity; change in velocity per time interval.
- Scalar — Quantity with magnitude only.
- Vector — Quantity with magnitude and direction.
- Displacement (( \Delta x )) — Change in position.
- Instantaneous velocity — Velocity at a specific instant.
- Average velocity — Total displacement divided by total time.
Action Items / Next Steps
- Practice solving velocity and acceleration problems using the given formulas.
- Review differences between scalar and vector quantities.
- Prepare for lessons on position vs. time and velocity vs. time graphs.