An 80 kg ball is on a flat, horizontal, straight path in Floobleland, where the acceleration of gravity is exactly 9.807 meters/sec/sec, and there is no friction or air resistance or any other such complication. Objects also have no rotating inertia.
How far does the ball roll (meters), and how long does it take to do so (seconds) if the ball starts at rest and the following 7 events occur in sequence? (Note: each event immediately follows the previous, and the final conditions for each are the initial conditions for the next).
1) A Flooble force causes a constant acceleration of 0.1 meters/sec/sec until its speed is 20 meters/sec
2) There is a Flooble zone that lowers the speed limit. Therefore, the ball does a constant deceleration to one half of its speed over a distance of 750 meters
3) A Floobleoid starts pushing the ball. This adds a 5 Newton assist to accelerate the ball for 320 seconds
4) The ball rolls off the edge of the Flooble Canyon, which is a sheer vertical cliff of height exactly 490.35 meter. After it hits the bottom in the flat and level Flooble Valley, it's vertical speed is immediately zero and it continues on for an additional 150 seconds
5) The ball encounters a Flooble battery and immediately gains 30 Watt-hours of kinetic energy. It then rolls on for 1200 meters
6) The ball encounters a null-Flooble-energy-field and experiences no forces of any kind for 60 seconds
7) The ball Flooble-decelerates at a constant rate to a stop in 15 seconds, or, maybe in 500 meters – whichever stops the ball more quickly.