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Learning Objectives: How are motion graphs interpreted?
1.7 POSITION, VELOCITY &
ACCELERATION VS TIME
GRAPHS
(Guided Notes)
1.3 Create and interpret graphs of 1-dimensional motion, such as position vs. time, distance vs. time, speed vs. time, velocity vs. time, and acceleration vs. time where acceleration is constant.
Understanding the definitions of velocity and acceleration allows us to create graphs which illustrate the motion. The mathematical definitions are as follows:
These definitions look a lot like the equation for the slope of a line used in math. This is because it is the slope of a line. The slope equation is: Slope of a line =
VELOCITY:
First recall how VELOCITY IS CALCULATED:
tinitial = 5 sec tfinal = 25 sec
Xinitial = 50 meters Xfinal = 450 meters
Plot the points on the graph and sketch the line created by the points. Estimate the points (This does not have to be accurate) Label each axis of the graph and give the graph a title.
_____ vs ______
Time (seconds)
Postion (meters)
ti = xi =
tf = xf =
How is velocity represented on the graph?
From this graph we can see that the position is:
final initial
final initial
t t
x x
t
x
final initial
final initial
t t
v v
t
v
ACCELERATION:
Remember how ACCELERATION IS CALCULATED?
tinitial = 5 sec tfinal = 15 sec
Vinitial = 50 meters/sec Xfinal = 250 meters/sec
Plot the points on the graph and sketch the line created by the points. Label the axis of the graph and give it a title.
________ vs _________ Time (seconds)
Velocity (m/s) ti = vi =
tf = vf =
How is the acceleration represented on the graph?
What does it mean if acceleration is positive? The velocity of the object is (speeding up or slowing down)
The acceleration vector and the velocity are pointing in ( the same or opposite) directions.
tinitial = 9 sec tfinal = 12 sec
Vinitial = 28 meters/sec Xfinal = 13 meters/sec
Plot the points on the graph and sketch the line created by the points. Label the axis of the graph and give it a title.
Time (seconds)
Velocity (m/s)
ti = vi =
tf = vf =
What does it mean if acceleration is negative? The velocity of the object is ___________________________
The acceleration vector and the velocity are ______________________
ACCELERATION OR DECELERATION?
FREE FALLING BODY
What happens to the velocity of an object that is allowed to fall, (This is called a Free Falling
Body)?
As the object falls the velocity will____________ at a _______________ rate.
What happens to the position of an object that is allowed to fall, (This is called a Free Falling
Body)?
As the object falls the position will____________ at a _______________ rate.
What will the following graphs look like:
ACCELERATION FROM THE VELOCITY GRAPH
The slope of the v vs t graph is the acceleration.
Here the velocity of the object is ____________ at a(n)
__________ rate.
Calculate the slope of the graph to find the ____________
LET’S SEE HOW THE ONE GRAPH CREATES THE NEXT.
EXAMPLE: X IS CONSTANT, OBJECT STAYS IN SAME PLACE
X vs t V vs t
t (sec) t (sec)
x (m) v (m/s)
final initial
final initial
t t
v v
t
v
X vs t
V vs t
t (sec)
v (m/s)
x (m)
t (sec)
a vs t
t (sec)
a (m/s)
The x vs t graph is constant so the v vs t graph will be (positive/negative/zero)
The v vs t graph is constant so the a vs t graph will be (positive/zero/negative)
EXAMPLE: X CHANGING, OBJECT IS MOVING
EXAMPLE: X CHANGING MORE QUICKLY AS TIME GOES ON
The x vs t graph is increasing at a constant rate so the v vs t graph will be (positive/negative/zero) and (increasing/decreasing/constant)
The v vs t graph is ____________ at a ________ rate so the a vs t graph will be (positive/negative/zero) and (increasing/decreasing/constant)
The x vs t graph is increasing at an increasing rate so the v vs t graph will be (positive/negative/zero) and (increasing/decreasing/constant)
The v vs t graph is increasing at a constant rate so the a vs t graph will be (positive/negative/zero) and (increasing/decreasing/constant)
X vs t
V vs t
t (sec)
v (m/s)
x (m)
t (sec)
a vs t
t (sec)
a (m/s)
X vs t
V vs t
t (sec)
v (m/s)
x (m)
t (sec)
a vs t
t (sec)
a (m/s^2 )
