Overview
This lecture introduces foundational physics concepts, including displacement, velocity, acceleration, projectile motion, Newton's laws, forces, and related calculations.
Distance and Displacement
- Distance is the total length traveled, regardless of direction; always positive (scalar).
- Displacement is the change in position from start to finish, including direction; can be positive or negative (vector).
- Displacement = final position โ initial position (ฮx = xf โ xi).
- Example: 8 m east then 3 m west; distance = 11 m, displacement = 5 m east.
Scalars vs. Vectors
- Scalar quantities have magnitude only (e.g., distance, speed).
- Vector quantities have both magnitude and direction (e.g., displacement, velocity).
Speed and Velocity
- Speed is how fast an object moves (scalar; always positive).
- Velocity is speed with direction (vector; can be positive or negative).
- Formula: d = vt (distance = speed ร time).
- 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 = โ2 m/s.
Acceleration
- Acceleration is the rate of change of velocity per unit time.
- Formula: a = (vf โ vi) / t.
- Positive acceleration = speeding up; negative acceleration = slowing down.
- If velocity and acceleration have the same sign, object speeds up; opposite signs, object slows down.
Gravitational Acceleration
- Earth's gravitational acceleration (g) = โ9.8 m/sยฒ (downward).
- g affects only the vertical (y) component of velocity, not horizontal (x).
- On the Moon, g = โ1.6 m/sยฒ.
Projectile Motion
- Projectile: object moving under gravity's influence.
- Motion analyzed separately in x (horizontal, constant velocity) and y (vertical, changing velocity) directions.
- vx (horizontal velocity) remains constant if no horizontal acceleration.
- vy (vertical velocity) changes by โ9.8 m/s every second due to gravity.
- At the highest point, vy = 0, vx unchanged.
Newton's Three Laws of Motion
- First Law (Inertia): Object at rest stays at rest, object in motion stays in motion unless acted upon by a force.
- Second Law: Net force = mass ร acceleration (F = ma).
- Example: 10 kg box, 80 N force โ acceleration = 8 m/sยฒ.
- Third Law: (Not included in this excerpt.)
Key Terms & Definitions
- Scalar โ Quantity with magnitude only (e.g., distance, speed).
- Vector โ Quantity with magnitude and direction (e.g., displacement, velocity).
- Displacement โ Change in position, includes direction.
- Speed โ Rate of distance covered, scalar.
- Velocity โ Speed in a given direction, vector.
- Acceleration โ Rate at which velocity changes.
- Projectile โ Object moving only under gravity's influence.
- Trajectory โ Path followed by a projectile.
- Gravitational Acceleration (g) โ Acceleration due to Earth's gravity, โ9.8 m/sยฒ.
Action Items / Next Steps
- Practice distinguishing scalar and vector quantities.
- Solve problems using d = vt and a = (vf โ vi)/t.
- Review Newton's Three Laws and apply them to real-world scenarios.
- Read next section on forces and momentum if assigned.