# Q & A: what is acceleration?

Q:
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. 1. What is the best graph representation of acceleration? One text shows constant acceleration as a straight line. (I understand that.)The other text STRESSES emphatically that acceleration should always be shown as a curved line on a graph. Is the only difference constant vs. not constant? 2. Im still having trouble understanding the concept that although acceleration in the direction of motion may be constant, the speed of the object will increase. I keep visualizing a penny being dropped of the Empire State Building. Assuming you did not hit the ground, would the speed of the falling object continue to increase infinitely? ( I have to think like an 8th grader.)
- Marsha (age 41)
Sevier Middle, Kingsport, TN
A:
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.

Mike W.

(published on 10/22/2007)

## Follow-Up #1: constant acceleration in relativity?

Q:
"If the acceleration were really constant, the speed would indeed increase toward infinity." The above quote, would that statement not be true because the speed could only reach the speed of light?
- Chris (age 57)
Glen Cove , NY 11542
A:
You're right that there's a speed limit, c. That means that constant acceleration can't go on for ever. You might ask what would happen if one had a rocket so that one felt a constant force for a long time. In the reference frame of somebody who's not accelerating but happens to be traveling along with you at some time, it looks like you have some fixed acceleration. But if you transform back to how that looks in the reference frame of somebody who you were at rest with initially, it looks like your acceleration keeps decreasing. It decreases so much that its integral, your net velocity in that starting frame, never quite reaches c.

Mike W

An example of this is the speed of particles in a high energy accelerator such as the LHC. No matter how much energy you pump in to the particles, your can never get them to move faster than the speed of light.

LeeH

(published on 03/29/2012)