Uniform Motion
t=0
t=1s
t=2s
t (s)
x (cm) v
(cm/s)
0
0.0
1.0
5.0
5
2.0
10.0
5
3.0
15.0
5
4.0
20.0
5
5.0
25.0
5
6.0
30.0
5
7.0
35.0
5
8.0
40.0
5
t=3s
t=4s
t=5s
t=6s
t=7s
t=8s
Non-uniform motion
t=1s t=3s
t=0
t=2s
t=4s t=5s
t=6s
t=7s
t=8s
t=9s
What is the velocity at t = 5.5 s?
t=1s t=3s
t=0
t=2s
t=4s t=5s
t=6s
t=7s
t=8s
t=9s
• All we know from the given data is the average velocity between t
= 5.0 and t = 6.0 s.
• Measure the object’s position at a smaller time interval, like t = 5.4
s and t = 5.6 s.
• Better yet, use t = 5.49 s and t = 5.51 s.
• The velocity at the instant t = 5.5 s is approximately equal to the
average velocity during a small time interval from t = 5.49 s to t =
5.51 s. But the best we can do with the given data is guess.
Chapter 2
Motion in 1-D
PHY211
Dr. Aaron Titus
Instantaneous Velocity
• The velocity at an instant of time is called
instantaneous velocity.
• It is approximately equal to the average velocity
measured during a very small time interval.
Position vs. time graph
t (s)
0
1.0
2.0
3.0
4.0
5.0
6.0
7.0
8.0
9.0
x (cm)
Position vs. time graph
t (s)
x (cm)
0
0.0
1.0
0.5
2.0
2.2
3.0
5.0
4.0
8.8
5.0
13.8
6.0
19.9
7.0
27.2
8.0
35.4
9.0
45
Position vs. time graph
-Slope of a tangent line
on an x vs. t graph is
instantaneous velocity.
-Sign of slope (pos or
neg) is direction of
motion.
-How slope changes
tells you whether it is
speeding up or slowing
down.
Example
Describe the motion of the object whose x vs. t
graph is shown below.
Example
Describe the motion of the object whose x vs. t
graph is shown below.
Velocity vs. time graph
t (s)
x (cm)
v
(cm/s)
0
0.0
1.0
0.5
0.5
2.0
2.2
1.8
3.0
5.0
2.8
4.0
8.8
3.8
5.0
13.8
5.0
6.0
19.9
6.1
7.0
27.2
7.3
8.0
35.4
8.2
9.0
45
9.6
QuickTime™ and a
TIFF (Uncompressed) decompressor
are needed to see this picture.
Velocity vs. time graph
t (s)
x (cm)
v
(cm/s)
0
0.0
1.0
0.5
0.5
2.0
2.2
1.8
3.0
5.0
2.8
4.0
8.8
3.8
5.0
13.8
5.0
6.0
19.9
6.1
7.0
27.2
7.3
8.0
35.4
8.2
9.0
45
9.6
Velocity vs. time graph
-Slope of v vs. t graph is
acceleration.
-acceleration is the rate
that the object speeds
up or slows down.
-if slope is constant, then
the motion is
characterized by
constant acceleration
Example
Describe the motion of the object whose v vs. t
graph is shown below.
QuickTime™ and a
TIFF (Uncompressed) decompressor
are needed to see this picture.
Example
Describe the motion of the object whose v vs. t
graph is shown below.
QuickTime™ and a
TIFF (Uncompressed) decompressor
are needed to see this picture.
Example
Describe the motion of the object whose v vs. t
graph is shown below.
QuickTime™ and a
TIFF (Uncompressed) decompressor
are needed to see this picture.
Observations
If the object’s velocity is positive and the object
speeds up, its acceleration is:
1. positive
2. negative
3. zero
Observations
If the object’s velocity is positive and the object
slows down, its acceleration is:
1. positive
2. negative
3. zero
Observations
If the object’s velocity is negative and the object
slows down, its acceleration is:
1. positive
2. negative
3. zero
Observations
If the object’s velocity is positive and the object
speeds up, its acceleration is:
1. positive
2. negative
3. zero
Matching position and velocity graphs
1. Note what is being plotted in a given graph.
2. Describe the motion in words or with a diagram.
3. Sketch (or match) the graph that matches the motion diagram
or verbal description of the motion.
QuickTime™ and a
TIFF (Uncompressed) decompressor
are needed to see this picture.
QuickTime™ and a
TIFF (Uncompressed) decompressor
are needed to see this picture.
v
t
0
x
The graph at left shows a moving
object’s velocity v vs clock reading t.
One of the graphs below shows the
object’s position x plotted vs t over the
same time interval. Which one is it?
A
B
x
0
t
0
x
0
0
t
D
x
t
C
x
0
t
E
t