Basic Concepts in Physics

1. Displacement vs. Distance

• Distance: A measure of how far an object has traveled. Eg: 100 miles between cities. (Scalar quantity: only magnitude)
• Displacement: Distance that includes direction. Eg: John walks 8 meters east then 3 meters west, displacement is 5 meters. (Vector quantity: magnitude and direction)
  • Final position minus initial position
  • Example: John (8m east, 3m west) — Displacement is 5m, Total distance is 11m.

2. Speed vs. Velocity

• Speed: How fast something is moving. (Scalar quantity: only magnitude)
  • Formula: d = vt (distance = speed x time)
  • Example: Car traveling 60 miles/hr, 300 miles in 5 hrs.
• Velocity: Speed with direction. (Vector quantity: magnitude and direction)
  • Can be positive or negative.
  • Example: Train moving 30m/s west (velocity).

Average Speed

• Formula: v_avg = total distance / total time
  • Example: Object travels 12m east, 20m west in 4s.
  • Total distance = 32m, average speed = 8m/s.

Average Velocity

• Formula: v_avg = displacement / total time
  • Example: Displacement = 12m + (-20m) = -8m in 4s.
  • Average velocity = -2m/s.

3. Acceleration

• Acceleration: Rate of change of velocity.
  • Example: Truck (0-60 in 30s) vs. sports car (0-60 in 5s).
• Formula: a = Δv / Δt
  • Example: Truck: Δv = 60 mi/h, Δt = 30s, a = 60/30 = 2 mi/h·s.
  • Sports car: Δv = 60 mi/h, Δt = 5s, a = 60/5 = 12 mi/h·s.
• Positive Acceleration: Velocity increases.
• Negative Acceleration: Velocity decreases.
• Example: Initial velocity 12m/s east, acceleration 4m/s²; velocities 16m/s after 1s, 20m/s after 2s, etc.

Acceleration Formula

• v_final = v_initial + at
  • Example: Initial velocity 24m/s east, acceleration -6m/s²; velocities 18m/s after 1s, 12m/s after 2s, etc.
  • Speed (absolute value of velocity) always positive.
• Opposite Signs: Decelerating.
• Same Signs: Accelerating.

4. Gravitational Acceleration

• Earth: g = -9.8 m/s²
• Moon: g = -1.6 m/s²
• Example: Ball dropped from rest, velocity after 1s = -9.8m/s, 2s = -19.6m/s, etc.
  • Positive/Negative Direction: Reflects up/down movement.

5. Projectile Motion

• Projectile: Object moving under the influence of gravity.
• One-dimensional: Motion only in y-direction (e.g., ball downward or upward, then downward).
• Two-dimensional: Motion in x and y directions (e.g., ball kicked off a cliff).
• Horizontal Component (v_x): Constant (no horizontal acceleration).
• Vertical Component (v_y): Changes due to gravity (g = -9.8m/s²).
• Symmetry: Speeds at same height are same but in opposite directions.

6. Newton's Three Laws of Motion

Newton's First Law

• An object at rest stays at rest, and an object in motion stays in motion unless acted upon by a net force.
  • Example: Box at rest needs a push to move.

Newton's Second Law

• Net force on an object is equal to the mass times the acceleration (F = ma).
  • Example: 10kg mass, force = 80N; acceleration = 80N/10kg = 8m/s².

Newton's Third Law

• For every action, there is an equal and opposite reaction.
• Example: Jumping off a boat – push boat back as you move forward.

7. Summary of Formulas

• Distance: d = vt
• Average Speed: v_avg = total distance / total time
• Average Velocity: v_avg = displacement / total time
• Acceleration: a = Δv / Δt
• Final Velocity: v_final = v_initial + at
• Net Force: F_net = ma