The position of a particle is described by r = (t3 + 4t − 4) mm and θ = (t3/2) rad, where t is in seconds. Determine the magnitudes of the particle’s velocity in m/s at the instant t = 2s.

Q1 A pendulum is modelled by a mass that is attached to a weightless rigid rod. According to Newton's second law, as the pendulum swings back and forth, the sum of the forces that are acting on the mass equals the mass times acceleration. The equilibrium equation in the tangential direction as: EF, -CL do dt -mg sin0 = mL Ld²o di² Where angle of the pendulum (with respect to the vertical axis, as shown in the figure) c=0.16(N-s)/m is the damping coefficient, m=0.5kg is the mass, L-1.2m is the length, and g-9.81m/s² is the acceleration due to gravity. The pendulum is initially displaced such that 0-90°, and then at t=0 it released from rest, = 0 (zero initial velocity). Determine the angle of the pendulum at 0.1 second using Runge-Kutta 2nd Order Method (Heun's method ) and step size (h=0.02). de dt 1-1-0 D 0 ។ K²₂² = f(tish, Off²h, 2; thks")

Part A Determine the magnitude of the particle's velocity when t = 4 s Express your answer to three significant figures and include the appropriate units.   Part B Determine the magnitude of the particle's acceleration when t = 4 s Express your answer to three significant figures and include the appropriate units.

The position of a particle moving along the x-axis is given by x (t) = 5.0 - 2.0t m. (a) at what time does the particle cross the origin? (b) what is the displacement of the particle between t = 4.0 s and t = 8.0 s?