Graphical Analysis of Motion
Physics 11
Graphing Motion
• Graphs are a powerful way of describing the
motion of an object.
• In motion, the following graphs are often
analyzed:
– Position-Time
– Velocity-Time
– Acceleration-Time
• This section will study the relationships
between these graphs.
Position-Time Graph
• A position-time graph shows where the object
in question is located at any point in time.
• A position-time graph will also give you the
object's average velocity over a period of time.
Slope in a Graph
Slope (given symbol m) for a x-y
graph equals:
𝑐ℎ𝑎𝑛𝑔𝑒 𝑖𝑛 𝑦 𝑦2 − 𝑦1
𝑚=
=
𝑐ℎ𝑎𝑛𝑔𝑒 𝑖𝑛 𝑥 𝑥2 − 𝑥1
In the case of a position-time graph,
the slope is :
∆𝑑
𝑚=
∆𝑡
which is the definition of average
velocity.
Example
Draw the velocity-time graph of the object in
motion described in the graph below:
Negative Velocities and Average Speed
• When the velocity of an object changes from
positive to negative (or vice versa), it means
that it has changed direction.
• On a position-time
graph, this occurs
at the maximums
and minimums.
Instantaneous Speed on a graph
• In reality graphs are rarely straight lines. You
then have to analyze curves.
• To find the instantaneous speed (or speed at a
specific time) on such a
graph, you need to
calculate the slope
of the tangent line
on that point.
Quick Practice
p.57 # 4
Velocity-Time Graph
• What do you obtain with the slope of a
velocity-time graph?
• How can you find the displacement of an
object using a velocity-time graph?
Example
Jonathan can run as shown in the graph below.
a) How fast is Jonathan running at:
– 1 second?
– 4 seconds?
– 5 seconds?
b) For all 3 sections in the
graph, find:
– Jonathan’s acceleration
– Jonathan’s displacement
Match the following graphs with
their corresponding description
Acceleration-Time Graph
• What does it mean when an object like a car
accelerates?
• Can acceleration increase or decrease?
Example
• Using the graph below, find for each segment:
– The object’s velocity
– The object’s displacement
• What assumptions do you have to make?
Jerk
• In physics, a jerk is the
rate of change of
acceleration.
Quick Practice
p.70 # 3, 5, 7