Graphing Velocity vs Time 

 Our study of 1-dimensional kinematics has been concerned with the multiple means by which the motion of objects can be represented. Such means include the use of words, the use of diagrams, the use of numbers, the use of equations, and the use of graphs. As we will learn, the specific features of the motion of objects are demonstrated by the shape and the slope of the lines on a velocity vs. time graph. The first part of this lesson involves a study of the relationship between the shape of a v-t graph and the motion of the object.

Plotting constant negative velocity 

 Now Image the ball rolling along a very, very long table (over 7 meters long) but moving backwards.  As the ball rolls along it's position is recorded after each second.  

 For every second the ball moves 1 meter further away from the origin but in the opposite direction, so it's  velocity is -1 meter per 1 second or -1 m/s 

 Plotting velocity verses time, the ball moves exactly -1 meter for every second, so after 1 second the ball is -1 meter; after 2 second the ball is -2 meters away; 3 seconds -3 meters; etc......  So the velocity is -1 meter per 1 second for every seconds. 

Plotting constant positive velocity 

Image a ball rolling along a very, very long table (over 7 meters long).  As the ball rolls along it's position is recorded after each second.  

For every second the ball moves 1 meter further away from the origin, so it's velocity is 1 meter per 1 second or 1 m/s 

Plotting velocity verses time, the ball moves exactly 1 meter for every second, so after 1 second the ball is 1 meter; after 2 second the ball is 2 meters away; 3 seconds 3 meters; etc......  So the velocity is 1 meter per 1 second for every seconds.