A poodle is about to begin chasing after a beagle at the dog park. At time t = 0, both dogs are at rest and the beagle is d = 3.5 m ahead of the poodle. At this instant, the poodle begins accelerating at a1 = 2.5 m/s2 and the beagle begins accelerating at a2 = 1.8 m/s2. How much time t does it take for the poodle to catch the beagle? (Assume that the dogs run in the same direction in a straight line, and that they maintain these accelerations until the beagle is caught.) As part of your representation, include a position vs. time plot that depicts both dogs. For the limit check, investigate what happens to t if the poodle's acceleration is nearly equal to the beagle's acceleration (a1 a2).