Overview
This lecture introduces fundamental physics concepts, focusing on motion (displacement, speed, velocity, acceleration, projectile motion) and Newton's laws, with clear distinctions between key terms and their applications.
Distance vs. Displacement
- Distance is the total length traveled regardless of direction; always positive (scalar).
- Displacement is the difference between final and initial positions, including direction (vector), and can be positive or negative.
- Example: 8 meters east then 3 meters west = distance 11 m, displacement 5 m east.
Scalars vs. Vectors
- Scalars have only magnitude (e.g., distance, speed).
- Vectors have both magnitude and direction (e.g., displacement, velocity).
Speed and Velocity
- Speed is how fast something moves (distance/time); always positive (scalar).
- Velocity is speed with direction (displacement/time); can be positive or negative (vector).
- Formula: ( d = vt ), where ( d ) is distance or displacement, ( v ) is speed or velocity, ( t ) is time.
Average Speed vs. Average Velocity
- Average speed = total distance / total time.
- Average velocity = displacement / total time.
- Example: 12 m east + 20 m west in 4 s → average speed = 8 m/s, average velocity = -2 m/s (west).
Acceleration
- Acceleration is how fast velocity changes (change in velocity/time).
- Formula: ( a = (v_f - v_i) / t ) where ( v_f ) is final velocity, ( v_i ) is initial velocity.
- Positive acceleration: speed increases; negative acceleration: speed decreases.
- If velocity and acceleration signs are the same, object speeds up; if opposite, it slows down.
Gravitational Acceleration
- On Earth, gravitational acceleration ( g = -9.8, m/s^2 ), acts downward (vertical or y direction).
- Only affects vertical velocity (( v_y )), not horizontal (( v_x )).
Projectile Motion
- Projectile: object moving under gravity only.
- Two-dimensional motion has constant ( v_x ) (if no horizontal acceleration) and changing ( v_y ) (due to gravity).
- At max height, ( v_y = 0 ), ( v_x ) unchanged.
- Formulas: ( v_{x,0} = v \cos\theta ), ( v_{y,0} = v \sin\theta ).
Newton’s Three Laws of Motion
- First Law (Inertia): An object stays at rest or in motion unless acted on by a net force.
- Second Law: ( F_{net} = m a ) (net force equals mass times acceleration).
- Third Law: Not covered in this transcript.
Key Terms & Definitions
- Distance — Total path length traveled (scalar).
- Displacement — Straight-line difference between initial and final positions (vector).
- Speed — How fast an object moves (distance/time; scalar).
- Velocity — Speed with direction (displacement/time; vector).
- Acceleration — Rate of change of velocity (vector).
- Scalar — Quantity with magnitude only.
- Vector — Quantity with magnitude and direction.
- Projectile — Object moving under gravity alone.
- Trajectory — Path a projectile follows.
- Tension — Force transmitted by a rope.
- Friction — Force opposing motion between surfaces.
Action Items / Next Steps
- Review and memorize formulas for speed, velocity, and acceleration.
- Practice distinguishing between scalar and vector quantities.
- Solve sample problems involving projectile motion and Newton’s second law.