Função Afim - Definição e Gráfico Resolução Professor Ferretto

1. General Kinematics of Particles\n \n The particle's position is a function of time as: \n x(t) = x₀ + v₀t + 0.5at² \n \n where: \n x₀ = Initial position \n v₀ = Initial velocity \n a = Acceleration \n t = Time \n \n \n Graphical Representation: \n x(t) = 0.5 at² \n 1) Kinematic Graphs \n 2) Motion diagrams \n \n For any motion equations: \n x(t) = x₀ + vt \n or \n v(t) = v₀ + at \n or \n x(t) = x₀ + [v₀ + v(t)] t/2 \n \n 1. Instantaneous velocity: \n v = lim(Δt->0) (Δx/Δt) = dx/dt \n \n 2. Average velocity: \n v_avg = Δx/Δt \n \n 3. Constant acceleration \n \n \n 2. Newton's Second Law \n \n F = ma, where: \n F = net force (N) \n m = mass (kg) \n a = acceleration (m/s²) \n \n \n 3. Work-Energy Principle \n \n W = ΔKE = KE_f - KE_i \n \n where: \n W = Work done \n KE = Kinetic Energy \n \n \n 4. Energy Conservation \n \n KE + PE = constant \n \n where: \n PE = Potential Energy \n \n \n 5. Gravitational Potential Energy \n \n PE = mgh \n \n where: \n g = 9.81 m/s² (acceleration due to gravity) \n \n \n 6. Projectile Motion \n \n For vertical: \n y(t) = y₀ + v₀yt - 0.5gt² \n For horizontal: \n x(t) = x₀ + v₀xt \n \n 7. Circular Motion \n \n v = ωr \n a_c = v²/r \n \n where: \n ω = angular velocity \n r = radius \n a_c = centripetal acceleration \n \n \n 8. Rotational Kinematics\n \n θ(t) = θ₀ + ω₀t + 0.5αt² \n \n where: \n θ = angle (rad) \n α = angular acceleration \n \n \n 9. Torque \n \n τ = rFsin(θ) \n \n where: \n τ = torque \n F = force \n \n 10. Simple Harmonic Motion \n \n x(t) = A cos(ωt + φ) \n \n where: \n A = amplitude \n φ = phase constant