Curvilinear Motion and Projectile Motion

Flashcards covering curvilinear motion, projectile motion, and related kinematic concepts.

Curvilinear Motion

Motion that occurs when a particle moves along a curved path, often in 2 or 3 dimensions.

Position Vector (r)

Used to determine the position of a particle, s(t), in curvilinear motion. Both its magnitude and direction are time-dependent.

Displacement (Δr)

The change in a particle's position during a time interval dt, represented as a vector: Δr = r' - r.

Average Velocity (v_avg)

During the time Δt, the average velocity of the particle can be determined as: v_avg = Δr/Δt

Instantaneous Acceleration (a)

The time-derivative of velocity, representing the rate of change in velocity of a particle: a = lim (Δt→0) Δv/Δt = dv/dt = d²r/dt²

Projectile

Any body that is given an initial velocity and then follows a path determined by the effects of gravitational acceleration and air resistance.

Trajectory

The path followed by a projectile.

Horizontal Motion of a Projectile

A uniform motion that is not affected by the vertical motion.

Vertical Motion of a Projectile

Affected by gravity (g), and its acceleration is constant.

Constant Acceleration Equations (Rectilinear)

v = v₀ + act, s = s₀ + v₀t + (1/2)act², v² = v₀² + 2a_c(s - s₀)