Okay, I was reading "Understanding Physics" and I was understanding everything until I got to this: What is the velocity of a rolling ball at a paticular moment? Consider the first second of time. During that second the ball has been rolling at an average velocity of 2 ft/sec. It began that first second of time at a slower velocity. In fact, since it started at rest, the velocity at the beginning (after 0 seconds, in other words) was 0 ft/sec. To get the average up to 2ft/sec, the ball must reach correspondingly higher velocities in the second half of the time interval. If we assume that the velocity is rising smoothly with time, it follows that if the velocity at the beginning of the time interval was 2 ft/sec less than average, then at the end of the time interval (after one second), it should be 2 ft/sec more than average, or 4 ft/sec. What I don't understand is how did was 4 ft/sec determined.