A solid cylinder of radius R and mass m is initally at rest on the bed of a truck. The distance from the center of the cylinder to the back of the truck is d. When the truck starts moving with a constant acceleration a, the cylinder begins to roll and eventually falls off the bed of the truck. The friction between the bed of the truck and the cylinder is sufficent to prevent slipping. Find (a) the time necessary for the cylinder to roll off the truck and (b) the distance the truck travles during this time.