Marsha- It's always a pleasure to help out with these teaching questions.
1. "I'm an eighth grade science teacher, and, unfortunately my students usually dread our physics unit. I'm trying to simplify explanations in the text, but then I end up confusing myself. "
Perhaps one of the texts is showing VELOCITY vs. time, which would be a straight line if acceleration were constant. You can think of the acceleration as the slope of that line. Constant acceleration means constant slope, i.e. a straight line.
Perhaps the other text was showing POSITION vs. time. Now the velocity is the slope of that plot- how much the position changes per little time change. If the acceleration is anything except zero, the velocity changes. That means the slope of position vs. time changes, so it isn't a straight line.
2. Good question. If the acceleration were really constant, the speed would indeed increase toward infinity. However, for a real penny off a tall building, the acceleration isn't constant. As the penny starts going fast, air friction makes an upward force on it, reducing the downward acceleration. The downward acceleration becomes very small and the velocity approaches a limit.
(republished on 07/11/06)