Overview
This lecture provides an introduction to fundamental concepts in physics, including displacement, velocity, acceleration, projectile motion, Newton's laws, forces, and momentum.
Distance and Displacement
- Distance is a scalar quantity; it measures how far an object travels, regardless of direction.
- Displacement is a vector quantity; it measures the change in position, including direction.
- Displacement = Final position − Initial position; can be positive or negative depending on direction.
- Distance is always positive, while displacement can be positive or negative.
Scalars and Vectors
- Scalar quantities have only magnitude (e.g., distance, speed).
- Vector quantities have both magnitude and direction (e.g., displacement, velocity).
Speed and Velocity
- Speed is a scalar; it tells how fast something is moving (distance/time), always positive.
- Velocity is a vector; it describes speed with direction and can be positive or negative.
- Speed = |Velocity|
- Average speed = Total distance / Total time.
- Average velocity = Displacement / Total time.
Example: Average Speed and Velocity Calculation
- Total distance traveled: add all path lengths (e.g., 12 m east + 20 m west = 32 m).
- Displacement: consider direction (e.g., 12 m east - 20 m west = -8 m).
- Average speed = 32 m / 4 s = 8 m/s (always positive).
- Average velocity = -8 m / 4 s = -2 m/s.
Acceleration
- Acceleration measures how quickly velocity changes over time.
- Formula: Acceleration = (Final velocity − Initial velocity) / Time.
- Positive acceleration increases velocity; negative acceleration decreases it.
- If acceleration and velocity signs are the same, the object speeds up; if opposite, it slows down.
Gravitational Acceleration
- Earth's gravitational acceleration (g) = -9.8 m/s² (acts downward, negative y direction).
- Only affects vertical (y) component of velocity, not horizontal (x).
Projectile Motion
- A projectile moves under the influence of gravity (typically ignoring friction).
- In projectile motion, horizontal velocity (vx) is constant if no horizontal force acts.
- Vertical velocity (vy) changes by -9.8 m/s each second due to gravity.
- At maximum height in projectile motion, vy = 0, but vx remains constant.
- Components: vx = v cos(θ), vy = v sin(θ).
Newton’s Laws of Motion
- 1st Law: An object at rest stays at rest, and an object in motion stays in motion unless acted upon by a force.
- 2nd Law: Net force = Mass × Acceleration (F = m·a).
- Forces cause acceleration; no net force means constant velocity (or rest).
- Example: 80 N force on 10 kg mass yields acceleration of 8 m/s².
Key Terms & Definitions
- Distance — Total path length traveled (scalar, no direction).
- Displacement — Change in position with direction (vector).
- Scalar — Quantity with magnitude only.
- Vector — Quantity with magnitude and direction.
- Speed — Rate of distance change (scalar).
- Velocity — Rate of displacement change with direction (vector).
- Acceleration — Rate of velocity change.
- Projectile — Object moving under gravity alone.
- Trajectory — Path followed by a projectile.
- Force — Push or pull causing acceleration.
- Tension — Force via rope or cable.
Action Items / Next Steps
- Review formulas: displacement, speed, velocity, acceleration, and force.
- Practice calculating average speed and velocity with direction.
- Prepare for upcoming topics: Newton's 3rd law and momentum.