P-T Slope
Constant Velocity
• Consider a car moving with a constant,
rightward (+) velocity - say of +10 m/s.
4/13/2015
Position-Time Graphs
2
Graph of Constant Velocity
• If the position-time
data for such a car
were graphed,
then the resulting
graph would look
like the graph at
the right.
4/13/2015
Position-Time Graphs
3
Constant Velocity
• Motion described as a constant, positive
velocity results in a line of constant and
positive slope when plotted as a positiontime graph.
4/13/2015
Position-Time Graphs
4
The Meaning of Slope of p-t
Graphs
• The slope of a position vs. time graph
reveals pertinent information about an
object's velocity. For example:
– a small slope = small velocity
– a negative slope = negative velocity
– a constant slope (straight line) = constant
velocity
– a changing slope (curved line) = changing
velocity (more on this later).
4/13/2015
Position-Time Graphs
5
Slope of a p-t Graph
• The actual slope value of any
straight line on a graph is the
velocity of the object.
• Slope = Velocity
4/13/2015
Position-Time Graphs
6
Example 1
• Consider a car moving with a constant
velocity of +10 m/s for 5 seconds. The
diagram below depicts such a motion.
4/13/2015
Position-Time Graphs
7
Graph-Example 1
• The position-time
graph would look like
the graph at the right.
• Note that during the
first 5 seconds, the
line on the graph
slopes up 10 m for
every 1 second along
the horizontal (time)
axis.
4/13/2015
Position-Time Graphs
8
Calculating Slope
 Pick two points on the line and determine their
coordinates.
 Determine the difference in y-coordinates of
these two points (rise).
 Determine the difference in x-coordinates for
these two points (run).
 Divide the difference in y-coordinates by the
difference in x-coordinates (rise/run or slope).
4/13/2015
Position-Time Graphs
9
Graph-Example 1
• Calculate the slope
y2 – y1 = df – di = rise
x2 – x1
tf – ti
run
50-0m = 50m = 10 m
5-0 s
5s
s
4/13/2015
Position-Time Graphs
10
Example 2
• Now consider a car moving at a constant
velocity of +5 m/s for 5 seconds, abruptly
stopping, and then remaining at rest (v = 0
m/s) for 5 seconds.
4/13/2015
Position-Time Graphs
11
Graph-Example 2
• slope = df – di
tf – ti
25-0m = 25m = +5 m
5-0 s
5s
s
• slope = df – di
tf – ti
25-25m = 0m =
10-5 s
5s
4/13/2015
0 m
s
Position-Time Graphs
12
Note
• A slope of zero means that
the object is at rest (not
moving).
4/13/2015
Position-Time Graphs
13
Slope Principle
• The principle is: the
slope of the line on a
position-time graph is
equal to the velocity
of the object.
• If the object is moving
with a velocity of +4
m/s, then the slope of
the line will be +4
m/s.
4/13/2015
Position-Time Graphs
14
3 Trials
4/13/2015
Position-Time Graphs
15
Interpretation of p-t Graphs
• Recall:
– On a p-t graph a negative slope means that
the object is moving in the negative direction.
– A positive slope means that the object is
moving in the positive direction.
– No slope (zero) means that the object is at
rest.
4/13/2015
Position-Time Graphs
16
Interpretation of p-t Graphs
• Calculate slope for
the following
timeframes:
• 0s – 10s
• 10s – 15s
• 15s – 40s
• 40s – 55s
4/13/2015
Position-Time Graphs
17