Rucete ✏ AP Physics C In a Nutshell
2. Kinematics
This chapter covers one-dimensional and two-dimensional motion, including velocity, acceleration, free fall, projectile motion, relative motion, and uniform circular motion (UCM). It explains the basic calculus-based derivations for uniformly accelerated motion and the relationships between position, velocity, and acceleration.
Instantaneous and Average Quantities
• Instantaneous velocity: v = dx/dt.
• Instantaneous speed: magnitude of instantaneous velocity.
• Instantaneous acceleration: a = dv/dt.
• Average velocity: v̄ = Δx/Δt (slope of position-time graph).
• Average speed: total distance divided by total time (different from magnitude of average velocity).
• Average acceleration: ā = Δv/Δt (slope of velocity-time graph).
Uniformly Accelerated Motion (UAM)
• Key equations for constant acceleration:
v = v₀ + at
x = x₀ + v₀t + (1/2)at²
v² = v₀² + 2a(x – x₀)
• Displacement is independent of the path taken; only depends on initial and final positions.
• Free fall is a special case of UAM with acceleration a = –g.
Graphs of Motion
• x(t) graph: shape depends on acceleration (parabola if a ≠ 0).
• v(t) graph: straight line if a is constant.
• a(t) graph: horizontal line if a is constant.
Free-Fall Problems
• Acceleration due to gravity: g ≈ 9.8 m/s² downward.
• At the peak of projectile motion, vertical velocity vy = 0.
• Symmetry in projectile motion: ascent and descent are mirror images in time and speed (opposite vy signs).
Two-Dimensional Motion
• Break motion into independent x- and y-components.
• Analyze each dimension separately using UAM equations.
• Vectors are recombined at the end to find total displacement, velocity, or acceleration.
Projectile Motion
• Horizontal motion: constant velocity (aₓ = 0).
• Vertical motion: uniform acceleration (aᵧ = –g).
• Range (horizontal distance traveled): R = (v₀²sin(2θ₀))/g
• Time of flight (for symmetric launch and landing): t = (2v₀sinθ₀)/g
• Maximum height: H = (v₀²sin²θ₀)/(2g)
Relative Motion
• Motion observations depend on the reference frame chosen.
• Velocity of A relative to B: vA/B = vA – vB
• Important for analyzing moving walkways, riverboats, and aircraft in wind.
Uniform Circular Motion (UCM)
• An object moving in a circle at constant speed still accelerates because its velocity direction changes.
• Centripetal acceleration (directed toward center): ac = v²/r
• Centripetal force: net force causing centripetal acceleration.
• Period (T): time for one complete revolution: T = (2πr)/v
• Frequency (f): number of revolutions per second: f = 1/T
In a Nutshell
Kinematics describes how objects move using calculus-based equations relating position, velocity, and acceleration. Whether dealing with straight-line motion, projectile paths, or circular trajectories, a component-wise approach and clear understanding of vector quantities are essential for solving problems in physics.