A spring with a 4 kg mass is resting on a horizontal frictionless table and is attached to a wall at the left end. It will stretch 0.5 m beyond its natural length when a force of 12 N is applied. If the spring begins at the equilibrium position and is pushed to the right with an initial velocity of 3 m/s, find the position of the mass after t seconds.

Afaulty model rocket moves in the xy-plane (the positive y direction is vertically upward). the rocket's acceleration has components ax(t) = ? t2 and ay(t) = ? ? ? t, where ? = 2.50 m/s4 , ? = 9.00 m/s2 , and ? = 1.40 m/s3 . at t = 0 the rocket is at the origin and has velocity ~v0 = v0x ? i + v0y ? j with v0x = 1.00 m/s and v0y = 7.00 m/s. (a) calculate the velocity and position vectors as functions of time. (b) what is the maximum height reached by the rocket? (c) sketch the path of the rocket. (d) what is the horizontal displacement of the rocket when it returns to y = 0?