Connecting Position, Velocity, and Acceleration
As you change the position of the slider, you are changing the value of as a function of time . The rate at which changes is , which we call velocity . The faster you change the position , the larger becomes. Changing position to the right creates a velocity that is positive, and vice-versa. So, as you move the slider to the right, the red velocity vector will point to the right. Its length will be proportional to the rate (speed) at which you are moving the slider.
Acceleration is defined as the rate at which velocity changes, so that . If the slider is not moving, or is moving at a perfectly steady rate, then there is no change in velocity, and thus there is no acceleration. If the slider speeds up, its velocity is increasing in the direction it is moving, and its acceleration will point in that same direction direction. If it slows down, its velocity is decreasing in the direction of motion, and the acceleration points in the opposite direction of the velocity.