Determening Acceleration using Velocity versus Time Graphs
Acceleration can be determined using a velocity versus time graph by calculating the slope of the line. Since slope can be positive, negative or zero acceleration can also be positive, negative, or zero.
If a velocitytime graph is a straight line then the slope will be constant and therefore the acceleration of the object will be constant. This acceleration will be equal to the instantaneous acceleration at any point on the graph and it will be equal to the average acceleration of the object over any period of time.
If a velocitytime graph is parabolic then the average acceleration over a period of time can be determined by
As you can see, you are really determining the slope of the straight line segment over the elapsed time.
Instantaneous acceleration can also be determined using a velocitytime graph that is parabolic by determining the slope of the tangent line at a specific moment.
For example:
Determine the instantaneous acceleration of the object at 7.0 s.
[C  Check, PPeek, HHelp]
As shown in the previous example, instantaneous acceleration can be determined using a velocitytime graph and calculating the slope of the tangent line at a specific moment. Instantaneous acceleration is also equal to the average acceleration at the halfway point of the calculated interval.
For example:
If the average acceleration of a Canadian Goose, over the interval of 1 s to 7 s, was 4.0 m/s^{2} [E] then the instantaneous acceleration of the Canadian Goose at 4 s would be 4.0 m/s^{2} [E].
