Overview
This lecture introduces fundamental physics concepts, focusing on motion, forces, and Newton's laws, with clear explanations of key terms and formulas.
Distance and Displacement
- Distance measures how far an object travels and is always positive (scalar quantity).
- Displacement considers both magnitude and direction (vector quantity).
- Displacement = final position − initial position; can be positive or negative.
- Example: Traveling 8 meters east then 3 meters west gives a distance of 11 meters, displacement of 5 meters east.
- Scalars have only magnitude; vectors have both magnitude and direction.
Speed and Velocity
- Speed is a scalar and always positive; measures how fast distance changes (e.g., meters/second).
- Velocity is a vector; measures how fast displacement changes and in which direction.
- Formula: distance = speed × time (d = vt).
- Speed = total distance / total time; velocity = displacement / total time.
- Speed is the absolute value of velocity; velocity can be negative (direction matters).
Average Speed and Average Velocity
- Average speed = total distance traveled ÷ total time taken.
- Average velocity = net displacement ÷ total time taken.
- Example: 12 meters east, 20 meters west, in 4 seconds: average speed = 8 m/s, average velocity = −2 m/s.
Acceleration
- Acceleration measures how fast velocity changes (vector).
- Formula: acceleration = (final velocity − initial velocity) ÷ time (a = (vf − vi)/t).
- Positive acceleration increases velocity; negative acceleration (deceleration) reduces velocity.
- Speed increases if velocity and acceleration have the same sign; decreases if signs are opposite.
- Example: Gravitational acceleration on Earth is −9.8 m/s² (downward).
Gravitational Acceleration
- Gravity only affects vertical (y) velocity, not horizontal (x) velocity.
- When an object is dropped, its vertical velocity increases negatively by 9.8 m/s each second.
- When thrown upwards, vertical velocity decreases by 9.8 m/s each second until it reverses.
Projectile Motion
- A projectile moves under the influence of gravity alone.
- Horizontal velocity (vx) is constant; vertical velocity (vy) changes with gravity.
- At any time t: vx = initial vx, vy = initial vy − (9.8 m/s²) × t.
- The trajectory is the path followed by a projectile; at max height, vy = 0.
Newton’s Three Laws of Motion
- First Law: Objects at rest stay at rest; objects in motion stay in motion unless acted on by a net force.
- Second Law: Net force = mass × acceleration (F = ma).
- Third Law: Not covered in detail in this segment.
- Friction opposes motion; without friction, objects continue moving indefinitely.
- Tension is the force through a rope or cable.
Key Terms & Definitions
- Distance — Total length traveled, regardless of direction (scalar).
- Displacement — Straight-line change from initial to final position with direction (vector).
- Speed — How fast distance changes; always positive (scalar).
- Velocity — How fast displacement changes; includes direction (vector).
- Acceleration — Rate of change of velocity; can be positive or negative (vector).
- Scalar — Quantity with only magnitude.
- Vector — Quantity with both magnitude and direction.
- Gravitational Acceleration (g) — Acceleration due to gravity, −9.8 m/s² on Earth.
- Projectile — Object moving under gravity’s influence only.
- Net Force — Sum of all forces acting on an object.
- Tension — Force transmitted through a rope or cable.
Action Items / Next Steps
- Practice distinguishing between distance and displacement in example problems.
- Calculate speed, velocity, and acceleration for sample scenarios.
- Memorize key formulas: d = vt, a = (vf − vi)/t, F = ma.
- Prepare for upcoming discussion on Newton’s Third Law and momentum.