MOTION ALONG A LINE


Given a function x(t) for the motion of an object, we can define the velocity of the object at any time by v_x(t) = dx/dt. That is, the velocity at any time is the derivative of the position function at that time. Remember that the derivative of a function at a certain point is the slope of the function at that point.



In the same way we can define the acceleration a_x = dv_x/dt.



Constant Acceleration Animation
Another animation!
A classic example of motion under constant acceleration is free fall. An unsupported object in the earth's atmosphere accelerates toward the center of the earth at 10 meters per second per second.

FREE FALL ANIMATION

For free fall, just replace x by y, and the acceleration a_x by the acceleration due to gravity, −g.
Chapter 3