Physics Kinematics: Motion, Velocity, and Acceleration

Fundamental Concepts of Motion

• Free Fall: Objects moving under the influence of gravity alone.
• Position: Defined by a frame of reference.
• Displacement: Measures the change in position (Δx or Δy).
• Motion: Relative movement described over time using velocity, speed, and acceleration.
• Average Speed: Total distance divided by total time.

Scalars and Vectors

• Scalars: Quantities described by magnitude alone.
• Vectors: Quantities described by both magnitude and direction.
• Distance: A scalar quantity referring to how much ground an object has covered.
• Displacement: A vector quantity referring to an object's overall change in position.
• Speed: A scalar quantity referring to how fast an object is moving.
• Velocity: A vector quantity referring to the rate at which an object changes position.
• Acceleration: A vector quantity defined as the rate at which an object changes velocity.

Circular Motion

• Circular Motion: Movement of an object along a circular path.
• Angular Displacement: The angle (θ) between two consecutive positions of a radius, expressed in radians.
• Radian: The angle subtended at the center of a circle by an arc equal in length to the radius (2π rad = one revolution).
• Period (T): The time taken to complete one revolution.

Kinematic Equations

Constant Velocity (No Acceleration)

x = x₀ + v · t

Uniform Rectilinear Motion (With Acceleration)

v_f = v₀ + a · t

x = x₀ + v₀ · t + ½ · a · t²

Free Fall

v = v₀ - g · t

h = h₀ + v₀ · t - ½ · g · t²

Uniform Circular Motion

θ = θ₀ + ω · t

v = ω · r

T = 2π / ω

Centripetal Acceleration: a_n = v² / r

Frequency: f = 1 / T