1793: "Velocity & Acceleration vs. Time"

0:00Imagine a car traveling down a straight road at 60 miles an hour. The speedometer barely moves. You're covering distance, but in one important sense, nothing's changing. That's key to understanding velocity and acceleration. Velocity describes how quickly position changes with time, including direction. Travel east at a constant 60 miles an hour, or 97 kilometers per hour, and your velocity it stays constant. On a velocity versus time graph, that appears as a horizontal line. The area underneath that line represents displacement. Travel at 60 miles an hour for a half hour, and you've moved 30 miles or 48 kilometers. Now, press the accelerator. If your velocity increases from 0 to 60 miles per hour in 10 seconds, the graph slopes upward,

1:00and that slope represents acceleration. How quickly velocity changes with time? Acceleration is measured in meters per second squared. An acceleration of 2 meters per second squared means velocity increased by 2 meters per second. Every second. But acceleration doesn't necessarily mean speeding up, and negative acceleration doesn't necessarily mean slowing down. If velocity and acceleration point in opposite directions, the object slows down. If they point in the same direction, even if both are negative, it speeds up. An acceleration versus time graph takes this one step further. A line above 0 means positive acceleration. A line at 0 means velocity is not changing, and a line below 0 means negative acceleration.

2:03And the area under an acceleration graph gives you the change in velocity. That connects the three graphs. The slope of the position versus time gives velocity. The slope of velocity versus time gives you acceleration. The areas work backward. Acceleration gives a change in velocity while velocity gives a change in position. Position tells you where you are. Velocity tells you how your position is changing. Position tells how that change itself is changing. These are interesting things with JC.