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Main Kinematics & Dynamics Speed & Velocity Lesson I.4.4 Unit I:Kinematics & Dynamics

Using Graphs to Determine Velocity - Lesson I.4.4

Key Terms:

Graphing | Velocity | Displacement | Position | Slope |IL, NUM, CCT

Position versus Time Graphs

Velocity can be determined using a position-time graph by calculating the slope of the line. Velocities (slope) can be zero, constant or continuously changing depending on the shape of the graph.

If a position-time graph is parabolic then the object does not have a constant velocity; however, the average velocity of the object over a period of time can be determined by

Vave Equation

Position vs Time Graph - Changing Velocity

As you can see, when you are calculating average velocity you are really determining the slope of the straight line segment over the elapsed time.

Position vs Time Graph - Changing Velocity - Slope
Slope Equation

Instantaneous velocity can also be determined using a position-time graph that is parabolic by determining the slope of the tangent line at a specific moment.

For example:

Determine the instantaneous velocity of the object at 7.0 s.


 
 
[C - Check, P-Peek, H-Help]
Slope =
[Rise]
=
[Run]

 

 

As shown in the previous example, instantaneous velocity can be determined using a position-time graph and calculating the slope of the tangent line at a specific moment.

For example:

If the average velocity of a Canadian Goose, over the interval of 10 s to 15 s, was 15 m/s [E] then the instantaneous velocity of the Canadian Goose at 12 s would be 15 m/s [E].

Velocity versus Time Graphs

Velocity can be determined directly by reading the information on a velocity-time graph.

Constant Velocity
This graph shows an object with constant velocity of 12 m/s [N].
Changing Velocity This graph displays an object with changing velocity. At 1 s its velocity is 4 m/s [N] and at 4 s its velocity is 16 m/s [N].

  
Rollercoaster




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