Basic Concepts in Physics

Introduction

• Covers basic concepts: displacement, velocity, acceleration, projectile motion, Newton's three laws, forces, momentum.
• Basic intro to physics principles.

Distance and Displacement

Distance

• Measure of how far something has traveled.
• Scalar quantity (only magnitude).
• Example: Distance between two cities = 100 miles.

Displacement

• Similar to distance but includes direction.
• Vector quantity (magnitude and direction).
• Example: John walks 8 meters east, then 3 meters west. Distance = 11 meters; Displacement = 5 meters (final position - initial position).
• Positive/negative sign indicates direction (east/north = positive, west/south = negative).

Key Differences

• Distance: Always positive, scalar quantity.
• Displacement: Can be positive or negative, vector quantity (e.g., 300 miles north).

Speed

Definition

• Tells how fast something is moving.
• Example: Car traveling 30 meters per second (covers 30 meters each second).

Formula

• Distance (d) = speed (v) × time (t).
• Example calculation for distance and time using formula (d = vt).

Speed vs Velocity

• Speed: Scalar, always positive.
• Velocity: Vector, can be positive or negative; includes direction.

Average Speed and Average Velocity

Average Speed

• Total distance divided by total time.
• Formula: v = d/t
• Example: Object travels 32 meters in 4 seconds; average speed = 8 m/s.

Average Velocity

• Total displacement divided by total time.
• Formula: v = displacement/t
• Example: Object displaced by -8 meters in 4 seconds; average velocity = -2 m/s.

Acceleration

Definition

• How fast the velocity is changing.
• Positive acceleration: Speed increasing.
• Negative acceleration: Speed decreasing.
• Formula: a = Δv/Δt or (v_f - v_i)/t

Example Calculation

• Truck: 0 to 60 mph in 30 s, a = 2 mph/s.
• Sports car: 0 to 60 mph in 5 s, a = 12 mph/s.

Concepts

• Positive acceleration: Velocity increases.
• Negative acceleration: Velocity decreases.

Projectile Motion

One-Dimensional Motion

• Y direction (Vertical): Example of ball dropped or thrown straight up.
• Vertical acceleration due to gravity (g = -9.8 m/s² on Earth).

Two-Dimensional Motion

• Motion in both x (horizontal) and y (vertical) directions.
• Example: Ball kicked off a cliff, vx constant, vy changes due to gravity.
• Formulas: vx = v cos(θ), vy = v sin(θ)

Key Points

• vx is constant; vy changes with time.
• Gravitational acceleration affects vy, not vx.

Newton's Three Laws

First Law

• An object at rest stays at rest; an object in motion stays in motion unless acted upon by a net force.
• Example: Box at rest/moving can only change state with applied force.

Second Law

• Force equals mass times acceleration (F = ma).
• Example: 10 kg mass with 80 N force accelerates at 8 m/s².

Third Law

• For every action, there is an equal and opposite reaction.
• Example: Box pushes back and exerts equal force in opposite direction.

Conclusion

• Covered displacement, velocity, acceleration, projectile motion, and Newton's laws.