Arace driver has made a pit stop to refuel. after refueling, he starts from rest and leaves the pit area with an acceleration whose magnitude is ; after he enters the main speedway. at the same instant, another car on the speedway and traveling at a constant velocity of overtakes and passes the entering car. the entering car maintains its acceleration. how much time is required for the entering car to catch the other car?

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?