Lesson 4 : Describing Motion
with Velocity vs. Time Graphs
Determining the Slope on a v-t
Graph
You learned earlier in Lesson
4 that the slope of the line on a velocity vs. time
graph is equal to the acceleration
of the object. If the object is moving with an
acceleration of +4 m/s/s (i.e., changing its velocity by
4 m/s each second), then the slope of the line will be +4
m/s/s. If the object is moving with an acceleration of -8
m/s/s, then the slope of the line will be -8 m/s/s. If
the object has an acceleration of 0 m/s/s, then the slope of the
line will be 0 m/s/s. The importance of slope in deciphering a velocity
vs. time graph means that a student of physics must have
a good understanding of how to calculate slopes.
This section of the lesson will discuss the method for
calculating the slope of a line on a velocity-time graph.
Let's begin by considering the velocity
vs. time graph below.
The line slopes upwards to the right. But
mathematically, by how much does it slope upwards along the vertical
(velocity) axis per 1
second along the horizontal (time) axis? To answer this
question use the slope equation:
The slope equation says that the slope
of a line is found by dividing the amount of
rise of the line between any two points by
the amount of run of the line between the same two
points. In other words:
1. Pick two points on the line and determine
their coordinates.
2. Determine the difference in y-coordinates of
these two points (rise).
3. Determine the difference in x-coordinates of
these two points (run).
4. Divide the difference in y-coordinates (rise) by the
difference in x-coordinates (run).
5. Slope = rise/run.
The calculation below applies this method
to determine the slope of the line in the graph above. Note
that three different calculations are performed for three
different sets of points on the line. In each case,
the result is the same: the slope is 10 m/s/s.
Check
Your Understanding
Consider the velocity-time graph below. Determine the
acceleration (i.e., slope) of the object as portrayed by
the graph. When you believe you know that value (and not
before), check the answer by clicking on the pop-up menu
below.
