Newtonian Mechanics Unit 1
Motion Graphs
Learning Goals
•Explain motion via words, math, or graphs
•Create, analyze, and interpret a position vs. time graph
•Create, analyze, and interpret a velocity vs. time graph
•Create, analyze, and interpret an acceleration vs. time graph
Setting up the graph
Your independent quantity always goes on the
horizontal axis (time is ALWYS independent)
The dependent quantity will go on the vertical axis
(position/velocity/acceleration).
The name of graphs ALWAYS follows the format
of dependent vs. independent
Math Class Connection
Slope of the graph will show how the dependent
value changes with respect to time.
The change associated with the slope of the line
could be the average velocity or average
acceleration (depending on the type of graph)
If the slope of the line is 0, then the dependent
value is constant (it may or may not have a value
of 0. Your graph will let you know)
Moving Man Simulation
Constant Position
Moving Man Simulation
Constant Velocity
Moving Man Simulation
Constant Acceleration
On a Position vs. Time
Graph
Location is easy
If the object is accelerating, the graph is a
parabola (open up +, open down -)
The slope of a line segment is the average velocity
between the end points on the segment (slope
determines direction of velocity)
To find the average velocity between two points
not on a segment use equation from velocity
definition
On a Position vs. Time
Graph
Instantaneous velocity (at a specific time) is found
by calculating the slop of the line segment
containing that time
If the graph is of acceleration (parabolic, therefore
no straight line segments) a tangent line will need
to be drawn and the slope will be taken of the
tangent line
On a velocity vs time
graph
Instantaneous velocity is easy
The slope of a line segment is the average
acceleration between the end points on the
segment (slope determines direction of velocity)
To find the average acceleration between two
points not on a segment use equation from
acceleration definition
On a Velocity vs. Time
Graph
Instantaneous acceleration (at a specific time) is
found by calculating the slop of the line segment
containing that time
If the graph has no straight line segments a
tangent line will need to be drawn and the slope
will be taken of the tangent line
Displacement is found by making shapes and
calculating the “area under the curve”