Overview
This lecture introduces the concepts of displacement, velocity, and acceleration in one-dimensional motion (kinematics), defining key terms, distinguishing vectors from scalars, and applying basic calculation methods with examples.
Displacement vs. Distance
- Displacement is a vector quantity (magnitude + direction), symbolized as Δx, representing the change in position.
- Distance is a scalar quantity (only magnitude), representing the total length traveled, regardless of direction.
- Displacement only considers the straight line from initial to final position; distance includes the entire path.
- SI unit for displacement and distance is the meter (m).
Velocity and Speed
- Velocity is a vector (magnitude + direction), defined as Δx/Δt (change in position over change in time).
- Speed is the scalar version, only magnitude, commonly used in everyday language.
- SI unit for velocity is meters per second (m/s).
- Average velocity with varying velocity: (initial velocity + final velocity)/2.
- Constant velocity means motion with unchanging speed and direction.
- Changing direction (even at constant speed) means velocity is not constant.
Acceleration
- Acceleration is a vector (magnitude + direction), defined as Δv/Δt (change in velocity over change in time).
- SI unit is meters per second squared (m/s²).
- Acceleration occurs when velocity changes (speed or direction).
- If acceleration and velocity are in the same direction, the object speeds up; if in opposite directions, the object slows down.
Interpreting Motion Graphs
- On position vs. time graphs: Slope = velocity.
- Horizontal line: zero velocity (no displacement).
- Positive slope: positive velocity (moving forward).
- Non-constant slope: velocity is changing.
- On velocity vs. time graphs: Slope = acceleration.
- Horizontal line: constant velocity (zero acceleration).
- Straight line (non-zero slope): constant (uniform) acceleration.
- Curved line: acceleration is changing (not constant).
Example Calculations
- Displacement in a complete circular revolution = 0 (start and end at same point).
- Displacement after half a revolution = diameter; find using circumference (C = πd).
- Average velocity = displacement/time, with direction (e.g., 60 mi/hr north).
- Acceleration = (final velocity - initial velocity)/time; units can be mph/s or m/s².
- Positive vs. negative acceleration distinguishes speeding up vs. slowing down.
Key Terms & Definitions
- Displacement (Δx) — Change in position; a vector with both magnitude and direction.
- Distance — Total length traveled; a scalar with only magnitude.
- Velocity (v) — Rate of change of displacement; a vector (Δx/Δt).
- Speed — Rate of change of distance; a scalar.
- Acceleration (a) — Rate of change of velocity; a vector (Δv/Δt).
Action Items / Next Steps
- Review motion graphs and practice distinguishing between displacement, velocity, and acceleration.
- Complete assigned study guide questions and check answers.
- Prepare for more complex problems involving direction and sign conventions in upcoming lessons.