Position vs. Time Analysis of a Position vs. Time Graph.
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Transcript of Position vs. Time Analysis of a Position vs. Time Graph.
Position vs. TimePosition vs. Time
Analysis of a Position vs. Time Analysis of a Position vs. Time GraphGraph
Determining the motion on a Determining the motion on a D vs. T GraphD vs. T Graph
Where did the object start?Where did the object start?
Which direction did it go?Which direction did it go?
Where did the object stop?Where did the object stop?
Is the motion uniform (constant)?Is the motion uniform (constant)?
Is the motion non-uniform (changing)?Is the motion non-uniform (changing)?
Can you tell which is faster? (if 2 or Can you tell which is faster? (if 2 or more objects are present)more objects are present)
Position vs. Time Graphs & Position vs. Time Graphs & VelocityVelocity
We can calculate velocity using We can calculate velocity using Position vs. Time GraphsPosition vs. Time Graphs
Velocity is a vector quantity because Velocity is a vector quantity because it has both magnitude & direction.it has both magnitude & direction.– It tells us not only the speed that an It tells us not only the speed that an
object is traveling, but also its directionobject is traveling, but also its direction
Distance RiseDistance Rise
Velocity = ----------- = -------Velocity = ----------- = -------
Time RunTime Run
Using slope to predict motionUsing slope to predict motionOn a On a distance vs. timedistance vs. time graph graph– If slope is 0, then velocity is 0.If slope is 0, then velocity is 0.– If slope is positive, velocity is If slope is positive, velocity is
constant in positive direction.constant in positive direction.– If slope is negative, velocity is If slope is negative, velocity is
constant in the opposite direction.constant in the opposite direction.– If slope is changing, velocity is If slope is changing, velocity is
changing.(i.e. you are changing.(i.e. you are accelerating)accelerating)
d(m)
t(s)
A
Object A is stationary at some positive position from the origin.
d(m)
t(s)
B
Object B moves Object B moves away from origin away from origin with a constant with a constant positive velocity.positive velocity.
d(m)
t(s)
C
Object C start at some positive position and moves away from the origin at a constant positive velocity.
d(m)
t(s)
D
Object D moves away from the origin at a constant positive velocity (slower than previous examples).
d(m)
t(s)
E
Object E start at some positive position and walks toward the origin with a constant velocity.
Distance vs. Time Graphs with Non-Uniform Motion
Changing velocity
(speeding up)
Changing velocity
(slowing down)
ExampleExample
d(m)
t(s)
A
B
D
C
Slower than B or C.
Same velocity as
B. V=0
Constant +V
PRACTICEPRACTICE
Practice #1
• Imagine you are riding your bike down Detroit Rd.
• Compare the lines A-D– Think of magnitude & direction!
Nagel Rd. (East)
Route 83/ Center Rd.
Stoney Ridge (West)
A
B
D
C
Practice #2• Determine the Time & Distances for the graph below
Time (s)
Position (m)
0
2.5
5
7.5
10
12.5
Practice #3• Calculate the velocities for the following:
East
Practice #4• Match the story to the graph below