The position of a particle as it moves along an y axis is given by y = (2.0cm)sin(πt/4), with t in second and y in centimeters. a. what is the average velocity of the particle between t = 0 and t = 2.0 s? b. what is the instantaneous velocity of the particle at t = 0, 1.0, and 2.0 s? c. what is the average acceleration of the particle between t = 0 and t = 2.0 s? d. what is the instantaneous acceleration of the particle at t = 0, 1.0, and 2.0 s?

Suppose that a mass of 2 kg is attached a spring whose spring constant is 50. the system is damped such that b = 12 . the mass is set in motion with an initial velocity of -8 m/s at a position 0 meters from equilibrium. set up and solve a differential equation that models this motion. write your solution in the form a cos ( ω t − α ) where α is a positive number. use your solution to fill in the information below: what is the amplitude of the motion? what is the value of ω ? what is the phase shift?