A flat-bed truck begins to drive away with a spool of cable loaded on the bed. The driver forgot to fasten the spool, and if he doesn't stop in time, the spool will roll off the back of the truck.

What is known:

• The truck accelerates at a = 1 m/s².
• The spool has a mass m = 140 kg, a radius r = 0.5 m, and a moment of inertia I = 17.5 kg-m².
• The spool can roll 3.5 m before it falls off the end of the truck.
• The spool rolls without slipping.

What is the acceleration of the center of gravity of the spool in the horizontal direction?

How long does the driver have before the spool rolls off the truck?

• Because the spool rolls, it exhibits both translational and rotational motion; thus, the equations developed in both the Translational Motion and Rotation about a Fixed Point sections will be needed to analyze the motion.
• Once the acceleration of the spool has been found, integrate that and the acceleration of the truck to find expressions for the positions of each, and use these to find the time it takes for the spool to reach the end of the truck.