Kinematics: Vector Magnitude, Velocity, and Projectile Motion (Vocabulary)

Vocabulary flashcards covering vector magnitude, vector angle, displacement, distance, velocity, acceleration, and projectile motion concepts from the lecture notes.

Vector Magnitude

The length (magnitude) of a vector; the resultant speed or total displacement, computed as the square root of the sum of the squares of its components (e.g., sqrt(x^2 + y^2)).

Vector Angle

The direction of a vector relative to the horizontal; given by θ = arctan(y/x).

Displacement

Change in position between initial and final points; Δx = xf − x0.

Distance

Total length of the path traveled, regardless of direction.

Average Velocity

The average rate of displacement over a time interval; calculated as Δx/Δt.

Instantaneous Velocity

The velocity at a specific moment; for constant acceleration, v = v0 + a t.

Position (Constant Acceleration)

Position as a function of time under constant acceleration: x = x0 + v0 t + (1/2) a t^2.

Velocity-Displacement (No Time)

Relationship between velocity and displacement without time: v^2 = v0^2 + 2 a (x − x0).

Free Fall

Vertical motion under gravity (g ≈ 9.8 m/s^2); y = y0 + v0 t − (1/2) g t^2 and v = v0 − g t.

Projectile Motion (2D)

Motion in two dimensions, with horizontal and vertical components; range and flight time depend on initial speed and launch angle (vx = v0 cosθ, vy = v0 sinθ − g t).

Horizontal Motion (No Acceleration)

Horizontal motion with constant velocity; x = x0 + v0x t.

Vertical Motion (Gravity Acts)

Vertical component of motion under gravity; y = y0 + v0y t − (1/2) g t^2 and v_y = v0y − g t.

Initial Velocity Components

Decompose initial speed into horizontal and vertical parts: v0x = v0 cos θ, v0y = v0 sin θ.

Range

Horizontal distance traveled by a projectile.

Flight Time

Time the projectile stays in the air before landing.

Trajectory

The path followed by a projectile through space.