Graphing Velocity verse Time 

     Now consider a ball moving with a rightward (+), changing velocity, that is, the ball that is moving rightward but speeding up or accelerating. The acceleration is 1 m/s/s or the velocity is increasing 1 m/s for every sec, so that the ball starts at rest but after 1 second the velocity 1 m/s; then after 2 seconds the velocity is 2 m/s; then 3 seconds 3 m/s; etc.............

 If the velocity-time data for such the ball were graphed, then the resulting graph would look like the graph at the right. Note that a motion described as a changing, positive velocity results in a sloped line when plotted as a velocity-time graph. The slope of the line is positive, corresponding to the positive acceleration. Furthermore, only positive velocity values are plotted, corresponding to a motion with positive velocity.

    The position of the ball over 5 seconds is  0 meters at 0 seconds; .5 meters at 1 second; 2 meters at 2 seconds; 4.5 meters at 3 secs; 8 meters at 4 seconds; and 12.5 meters at 5 seconds.

Velocity Verses Time 

Position Verses Time 

 The velocity vs. time graphs for the two types of motion - constant velocity and changing velocity (acceleration) - can be summarized as follows.

Constant Positive Velocity

Constant Negative Velocity 

With a constant velocity (both negative and positive constant velocity) is a result in of a zero acceleration, that is, without and acceleration the velocity can not change.

Changing Velocity 

Changing Velocity with a Positive Acceleration

 Changing Velocity with a Negative Acceleration

Because the object is accelerating then it must have a changing velocity.  Now there are many misconceptions when dealing with acceleration, first negative acceleration does not mean its decelerating. Take the graph on the right, the object has a negative acceleration but isn't decelerating. Looking at the data point the object is at rest then moving at -1 m/s then -2 m/s then after 5 secs it's moving at -5 m/s.  The speed of the object is growing and it's velocity is increasing negative which simply means it's going faster and faster in the negative direction.