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Different Position. Vs. Time graphs
Position vs. Time
Uniform Motion
Position (m)
20
Accelerated
Motion
15
10
5
0
1
2
3
4
5
6
7
8
9
10
Time (s)
Constant positive velocity
(zero acceleration)
Increasing positive velocity
(positive acceleration)
Position vs. Time
Position (m)
25
20
15
10
5
0
1
2
3
4
5
6
7
8
9
10
Time (s)
Constant negative velocity
(zero acceleration)
Decreasing negative velocity
(positive acceleration)
Different Position. Vs. Time
Changing slope means changing velocity!!!!!!
Decreasing negative slope = ??
Increasing negative slope = ??
x
B
A
t
C
A … Starts at home (origin) and goes forward
slowly
B … Not moving (position remains constant as time
progresses)
C … Turns around and goes in the other direction
quickly,
passing up home
During which intervals was he traveling in a positive direction?
During which intervals was he traveling in a negative direction?
During which interval was he resting in a negative location?
During which interval was he resting in a positive location?
During which two intervals did he travel at the same speed?
A) 0 to 2 sec B) 2 to 5 sec C) 5 to 6 sec D)6 to 7 sec E) 7 to 9 sec F)9 to 11 sec
x
B
C
Graphing w/
Acceleration
t
A
D
A … Start from rest south of home; increase speed gradually
B … Pass home; gradually slow to a stop (still moving north)
C … Turn around; gradually speed back up again heading south
D … Continue heading south; gradually slow to a stop near the
starting point
Tangent
Lines
x
t
On a position vs. time graph:
SLOPE
VELOCITY
SLOPE
SPEED
Positive
Positive
Steep
Fast
Negative
Negative
Gentle
Slow
Zero
Zero
Flat
Zero
Increasing &
Decreasing
x
t
Increasing
Decreasing
On a position vs. time graph:
Increasing means moving forward (positive direction).
Decreasing means moving backwards (negative direction).
x
Concavity
t
On a position vs. time graph:
Concave up means positive acceleration.
Concave down means negative acceleration.
x
Q
R
P
Special
Points
S
Inflection Pt.
P, R
Peak or
Valley
Q
Time Axis
Intercept
P, S
Change of concavity,
change of acceleration
Turning point, change of
positive velocity to
negative
Times when you are at
“home”, or at origin
t
Velocity vs time
Different Velocity-time graphs
Different Velocity-time graphs
Velocity vs. Time
Velocity (m/s)
20
15
10
5
0
1
2
3
4
5
6
7
8
9
10
7
8
9
10
Time (s)
Velocity vs. Time
Velocity (m/s)
25
20
15
10
5
0
1
2
3
4
5
6
Time (s)
Velocity vs. Time
Horizontal lines = constant velocity
 Sloped line = changing velocity

 Steeper
= greater change in velocity per
second
 Negative slope = deceleration
Acceleration vs. Time
Acceleration vs. Time
12
10
Acceleration (m/s^2)
Time is on the x-axis
 Acceleration is on
the y-axis
 Shows how
acceleration
changes over a
period of time.
 Often a horizontal
line.
8
6
4
2
0
1
2
3
4
5
6
Time (s)
7
8
9
10
x
All 3 Graphs
t
v
t
a
t
Real life
Note how the v graph is pointy and the a graph skips. In real life,
the blue points would be smooth curves and the orange segments
would be connected. In our class, however, we’ll only deal with
constant acceleration.
v
t
a
t
Constant Rightward Velocity
Constant Leftward Velocity
Constant Rightward
Acceleration
Constant Leftward Acceleration
Leftward Velocity with
Rightward Acceleration
Graph Practice
Try making all three graphs for the following scenario:
1. Newberry starts out north of home. At time zero he’s
driving a cement mixer south very fast at a constant speed.
2. He accidentally runs over an innocent moose crossing
the road, so he slows to a stop to check on the poor moose.
3. He pauses for a while until he determines the moose is
squashed flat and deader than a doornail.
4. Fleeing the scene of the crime, Newberry takes off again
in the same direction, speeding up quickly.
5. When his conscience gets the better of him, he slows,
turns around, and returns to the crash site.