Embed Size (px)
Citation preview
Uniform Motiont = 0 t = 1 s t = 2 s t = 3 s t = 4 s t = 5 s t = 6 s t = 7 s t = 8 s
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
Non-uniform motion
t = 0t = 1 s
t = 2 st = 3 s
t = 4 s t = 5 s t = 6 s t = 7 s t = 8 s t = 9 s
What is the velocity at t = 5.5 s?
• 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 2Motion in 1-D
PHY211Dr. Aaron Titus
t = 0t = 1 s
t = 2 st = 3 s
t = 4 s t = 5 s t = 6 s t = 7 s t = 8 s t = 9 s
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) x (cm)
0
1.0
2.0
3.0
4.0
5.0
6.0
7.0
8.0
9.0
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 aTIFF (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 aTIFF (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 aTIFF (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 aTIFF (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 aTIFF (Uncompressed) decompressor
are needed to see this picture.
QuickTime™ and aTIFF (Uncompressed) decompressor
are needed to see this picture.
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?
v
t0
t t t
tt
A B C
D E
00
00 0
x xx
x x
