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Physics 20: Kinematics

eMATH Activity

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Alternative Method of Producing a Velocity-Time Graph

Purpose:

To create a velocity-time data table and plot a velocity-time graph from a set of position-time data values.

Background:

An object’s motion can be recorded as a set of position-time values in a position-time chart.  This chart can be used to plot a position-time graph and a corresponding velocity-time graph.

The average velocity of an object is given by the equation v=d/t.  The average velocity can be computed for each time interval on a position-time graph by taking the change in displacement between two successive time intervals and dividing it by the change in time.  For example, the average velocity for the following position-time data table can be determined by as follows:

Position
(m)
Time
(s)
0.0 0.0
5.0 1.0
10.0 2.0

Average velocity for the time interval from 0.0 s to 1.0 s:

The average velocity for the time interval from 0.0 s to 1.0 s is 5.0 m/s.

Average velocity for the time interval from 0.0 s to 1.0 s:

The average velocity for the time interval from 1.0 s to 2.0 s is 5.0 m/s.

This method can be used for each successive time interval on a position-time table.  But the average velocity is for the entire time interval. So how do we plot a velocity-time graph for a specific time?  The answer lies in an interesting fact:

For an object undergoing a constant acceleration, the average velocity for a time interval is the same as the instantaneous velocity at the midpoint of the time interval.

This means that the average velocity from 0.0 s to 1.0 s is the same as the instantaneous velocity at the midpoint of the interval, or 0.5 s.  We can use this knowledge to create a velocity-time table, and from there, plot a velocity-time graph.

Instructions:

1. Download and open the accompanying Excel spreadsheet and use the position-time table given to create a velocity-time table:

Remember to create the table with the midpoint times for each interval as shown above.  Print this spreadsheet page with the completed velocity-time table.
2. From the velocity-time table plot the velocity-time graph using a graphing calculator or graphing program.  Print this graph.
3. Determine the slope of the resulting velocity-time graph to find the acceleration of the object.  Record the value that you found for the acceleration on the velocity-time graph.

Analysis:

1. What is the velocity of the object when the displacement is 0?
2. Why is there one less point to be plotted on the velocity-time graph than on the displacement-time graph?
3. What advantages can you see with regard to this method compared to taking the slopes of the tangents to the line?
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