LAB3.6: 1-D Kinematics – Relationships Between Position-Time and Velocity-Time Graphs
Name: _________________________________Class Period: ______ Date: __________
PURPOSE
The purpose of this activity is to establish the relationships between Position-Time and VelocityTime graphs for objects that are “just moving along” as well as those that are “going faster and
faster”.
BACKGROUND
In Laboratory 3.5, data was collected for an object that was “just moving along” as well one that
was “going faster and faster”. The following relationships should have been noted for the data
collected during that Laboratory:
 SCENARIO A - A recording where the object seemed, to the naked eye, to be “just
moving along” in a straight line:
o Position-Time Graph – constant slope
o Velocity-Time Graph – relatively constant
 SCENARIO B- A recording where the object seemed, to the naked eye, to be “going
faster and faster” in a straight line:
o Position-Time Graph – getting steeper and steeper as time proceeds
o Velocity-Time Graph – relatively constant slope
Evaluating slopes and areas from the graphs enables these graphs to be connected in ways that
generalizes to the position-time and velocity-time graphs for all moving objects.
PROCEDURE
1. Critique the position-time (x-t) and velocity-time (v-t) graphs printed during Laboratory
3.5 to determine if they sufficiently represent the relationships indicated in the
background section above. If either one or both of the scenarios is not reasonably close
to showing the expected relationships, obtain corresponding data from your teacher that
does show the expected relationships.
2. SCENARIO A Graphs: (Note: Show all work on graphs)
a. Position-Time Graph:
i. Use a straight edge to draw a best fit straight line through the data.
ii. Identify the points at the beginning and end of the best fit straight line
and use those points to calculate the slope of the best fit straight line (be
certain to include units for this and all other calculations).
b. Velocity-Time Graph:
i. Use a straight edge to draw a horizontal straight line that best
approximates the average velocity for the data.
ii. Calculate the area between the time axis and the horizontal straight line
that best approximates the average velocity for the data for the first and
second halves of the time interval for the motion.
3. SCENARIO B Graphs:
a. Position-Time Graph:
i. Use a straight edge to draw a straight line that just brushes the curve
(also called a tangent line) near the center of the time over which data
was collected.
ii. Calculate the slope of the tangent line
b. Velocity-Time Graph:
i. Use a straight edge to draw a best fit straight line through the data.
ii. Calculate the area between the time axis and the best fit straight line for
the first and second halves of the time interval for the motion.
DATA
Complete the following Tables:
SCENARIO A: “Just Moving Along”
x-t graph: slope of best fit straight line
v-t graph: estimate of average velocity
x-t graph: change in x during first half of
motion
v-t graph: area under graph during first half of
motion
x-t graph: change in x during second half of
motion
v-t graph: area under graph during second half
of motion
SCENARIO B: “Going Faster and Faster”
x-t graph: slope of best fit straight line
v-t graph: estimate of average velocity
x-t graph: change in position during first half
of motion
v-t graph: area under graph during first half of
motion
x-t graph: change in position during second
half of motion
v-t graph: area under graph during second half
of motion
ANALYSIS/CONCLUSIONS
Complete the following statements, based upon your analysis of the information in the DATA Section:

The slope of the position-time graph is equal to
____________________________________

The area under the velocity-graph is equal to
____________________________________

A velocity-time graph can be sketched directly from a position-time graph by
______________
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
A position-time graph can be sketched directly from a velocity-time graph by
______________
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