Chapter 2 Motion in one dimension. s, v, a Displacement: ( m ) Where you are Velocity: ( m/s ) The...
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Transcript of Chapter 2 Motion in one dimension. s, v, a Displacement: ( m ) Where you are Velocity: ( m/s ) The...
![Page 1: Chapter 2 Motion in one dimension. s, v, a Displacement: ( m ) Where you are Velocity: ( m/s ) The rate of change of displacement Acceleration: ( m/s.](https://reader035.fdocuments.in/reader035/viewer/2022062321/56649f285503460f94c40068/html5/thumbnails/1.jpg)
Chapter 2Motion in one dimension
![Page 2: Chapter 2 Motion in one dimension. s, v, a Displacement: ( m ) Where you are Velocity: ( m/s ) The rate of change of displacement Acceleration: ( m/s.](https://reader035.fdocuments.in/reader035/viewer/2022062321/56649f285503460f94c40068/html5/thumbnails/2.jpg)
s, v, a
Displacement: (m)Where you are
Velocity: (m/s)The rate of change of displacement
Acceleration: (m/s2)The rate of change of velocity
Note: Your textbook use x instead of s
![Page 3: Chapter 2 Motion in one dimension. s, v, a Displacement: ( m ) Where you are Velocity: ( m/s ) The rate of change of displacement Acceleration: ( m/s.](https://reader035.fdocuments.in/reader035/viewer/2022062321/56649f285503460f94c40068/html5/thumbnails/3.jpg)
Equations
![Page 4: Chapter 2 Motion in one dimension. s, v, a Displacement: ( m ) Where you are Velocity: ( m/s ) The rate of change of displacement Acceleration: ( m/s.](https://reader035.fdocuments.in/reader035/viewer/2022062321/56649f285503460f94c40068/html5/thumbnails/4.jpg)
Quick Examples
![Page 5: Chapter 2 Motion in one dimension. s, v, a Displacement: ( m ) Where you are Velocity: ( m/s ) The rate of change of displacement Acceleration: ( m/s.](https://reader035.fdocuments.in/reader035/viewer/2022062321/56649f285503460f94c40068/html5/thumbnails/5.jpg)
Useful facts about slopey
x0
![Page 6: Chapter 2 Motion in one dimension. s, v, a Displacement: ( m ) Where you are Velocity: ( m/s ) The rate of change of displacement Acceleration: ( m/s.](https://reader035.fdocuments.in/reader035/viewer/2022062321/56649f285503460f94c40068/html5/thumbnails/6.jpg)
The Signs of Slope (m)
m >0 m <0m =0
![Page 7: Chapter 2 Motion in one dimension. s, v, a Displacement: ( m ) Where you are Velocity: ( m/s ) The rate of change of displacement Acceleration: ( m/s.](https://reader035.fdocuments.in/reader035/viewer/2022062321/56649f285503460f94c40068/html5/thumbnails/7.jpg)
Slope = ± Rise over Run
![Page 8: Chapter 2 Motion in one dimension. s, v, a Displacement: ( m ) Where you are Velocity: ( m/s ) The rate of change of displacement Acceleration: ( m/s.](https://reader035.fdocuments.in/reader035/viewer/2022062321/56649f285503460f94c40068/html5/thumbnails/8.jpg)
Alternatively
You need two points to find a slope!
![Page 9: Chapter 2 Motion in one dimension. s, v, a Displacement: ( m ) Where you are Velocity: ( m/s ) The rate of change of displacement Acceleration: ( m/s.](https://reader035.fdocuments.in/reader035/viewer/2022062321/56649f285503460f94c40068/html5/thumbnails/9.jpg)
Find the slopes
![Page 10: Chapter 2 Motion in one dimension. s, v, a Displacement: ( m ) Where you are Velocity: ( m/s ) The rate of change of displacement Acceleration: ( m/s.](https://reader035.fdocuments.in/reader035/viewer/2022062321/56649f285503460f94c40068/html5/thumbnails/10.jpg)
Important: Unit of Slope!!!
Do not ignore the units! Different graph has different units.
Unit of slope = (unit of y-axis) / (unit of x-axis)
![Page 11: Chapter 2 Motion in one dimension. s, v, a Displacement: ( m ) Where you are Velocity: ( m/s ) The rate of change of displacement Acceleration: ( m/s.](https://reader035.fdocuments.in/reader035/viewer/2022062321/56649f285503460f94c40068/html5/thumbnails/11.jpg)
Unit of Slope!!!Unit of slope = (unit of y-axis) / (unit of x-axis)
![Page 12: Chapter 2 Motion in one dimension. s, v, a Displacement: ( m ) Where you are Velocity: ( m/s ) The rate of change of displacement Acceleration: ( m/s.](https://reader035.fdocuments.in/reader035/viewer/2022062321/56649f285503460f94c40068/html5/thumbnails/12.jpg)
Three graphs
slope slope
area area
![Page 13: Chapter 2 Motion in one dimension. s, v, a Displacement: ( m ) Where you are Velocity: ( m/s ) The rate of change of displacement Acceleration: ( m/s.](https://reader035.fdocuments.in/reader035/viewer/2022062321/56649f285503460f94c40068/html5/thumbnails/13.jpg)
Summary
![Page 14: Chapter 2 Motion in one dimension. s, v, a Displacement: ( m ) Where you are Velocity: ( m/s ) The rate of change of displacement Acceleration: ( m/s.](https://reader035.fdocuments.in/reader035/viewer/2022062321/56649f285503460f94c40068/html5/thumbnails/14.jpg)
Find the velocity at t = 1s, 2s
Hint: Find the slope
![Page 15: Chapter 2 Motion in one dimension. s, v, a Displacement: ( m ) Where you are Velocity: ( m/s ) The rate of change of displacement Acceleration: ( m/s.](https://reader035.fdocuments.in/reader035/viewer/2022062321/56649f285503460f94c40068/html5/thumbnails/15.jpg)
At t = 1s
![Page 16: Chapter 2 Motion in one dimension. s, v, a Displacement: ( m ) Where you are Velocity: ( m/s ) The rate of change of displacement Acceleration: ( m/s.](https://reader035.fdocuments.in/reader035/viewer/2022062321/56649f285503460f94c40068/html5/thumbnails/16.jpg)
At t = 2s
![Page 17: Chapter 2 Motion in one dimension. s, v, a Displacement: ( m ) Where you are Velocity: ( m/s ) The rate of change of displacement Acceleration: ( m/s.](https://reader035.fdocuments.in/reader035/viewer/2022062321/56649f285503460f94c40068/html5/thumbnails/17.jpg)
The sign of slope
![Page 18: Chapter 2 Motion in one dimension. s, v, a Displacement: ( m ) Where you are Velocity: ( m/s ) The rate of change of displacement Acceleration: ( m/s.](https://reader035.fdocuments.in/reader035/viewer/2022062321/56649f285503460f94c40068/html5/thumbnails/18.jpg)
Find the acceleration at t = 1s, 3s, 5.7s, 6.5s, 8s, 10s
Hint: Find the slopes at these times.
Vel
ocity
(m
/s)
![Page 19: Chapter 2 Motion in one dimension. s, v, a Displacement: ( m ) Where you are Velocity: ( m/s ) The rate of change of displacement Acceleration: ( m/s.](https://reader035.fdocuments.in/reader035/viewer/2022062321/56649f285503460f94c40068/html5/thumbnails/19.jpg)
Find a at t = 1s, 3s, 5.7s, 6.5s, 8s, 10sV
eloc
ity (
m/s
)
![Page 20: Chapter 2 Motion in one dimension. s, v, a Displacement: ( m ) Where you are Velocity: ( m/s ) The rate of change of displacement Acceleration: ( m/s.](https://reader035.fdocuments.in/reader035/viewer/2022062321/56649f285503460f94c40068/html5/thumbnails/20.jpg)
Instantaneous velocity versus average velocity
All the velocity we dealt with so far are “instantaneous velocity”, not “average velocity”.
Unless stated explicitly, velocity in general means “instantaneous velocity”.
![Page 21: Chapter 2 Motion in one dimension. s, v, a Displacement: ( m ) Where you are Velocity: ( m/s ) The rate of change of displacement Acceleration: ( m/s.](https://reader035.fdocuments.in/reader035/viewer/2022062321/56649f285503460f94c40068/html5/thumbnails/21.jpg)
Which is which?Questions about velocity are asked in either one of the two ways:
![Page 22: Chapter 2 Motion in one dimension. s, v, a Displacement: ( m ) Where you are Velocity: ( m/s ) The rate of change of displacement Acceleration: ( m/s.](https://reader035.fdocuments.in/reader035/viewer/2022062321/56649f285503460f94c40068/html5/thumbnails/22.jpg)
Average v or Instantaneous v?
![Page 23: Chapter 2 Motion in one dimension. s, v, a Displacement: ( m ) Where you are Velocity: ( m/s ) The rate of change of displacement Acceleration: ( m/s.](https://reader035.fdocuments.in/reader035/viewer/2022062321/56649f285503460f94c40068/html5/thumbnails/23.jpg)
Displacement and Area
![Page 24: Chapter 2 Motion in one dimension. s, v, a Displacement: ( m ) Where you are Velocity: ( m/s ) The rate of change of displacement Acceleration: ( m/s.](https://reader035.fdocuments.in/reader035/viewer/2022062321/56649f285503460f94c40068/html5/thumbnails/24.jpg)
Find the area
How far has the object traveled from 0s to 4s?
![Page 25: Chapter 2 Motion in one dimension. s, v, a Displacement: ( m ) Where you are Velocity: ( m/s ) The rate of change of displacement Acceleration: ( m/s.](https://reader035.fdocuments.in/reader035/viewer/2022062321/56649f285503460f94c40068/html5/thumbnails/25.jpg)
Watch out for negative area!V
elo
city
(m
/s)
Time (s)0
1m/s
-1m/s
2s 4s
If a line goes under the x-axis, the area it encloses is treated as negative.
+
-
![Page 26: Chapter 2 Motion in one dimension. s, v, a Displacement: ( m ) Where you are Velocity: ( m/s ) The rate of change of displacement Acceleration: ( m/s.](https://reader035.fdocuments.in/reader035/viewer/2022062321/56649f285503460f94c40068/html5/thumbnails/26.jpg)
Change of velocity is the area under the acceleration-
time curve
+-
![Page 27: Chapter 2 Motion in one dimension. s, v, a Displacement: ( m ) Where you are Velocity: ( m/s ) The rate of change of displacement Acceleration: ( m/s.](https://reader035.fdocuments.in/reader035/viewer/2022062321/56649f285503460f94c40068/html5/thumbnails/27.jpg)
If you don’t already know this…
![Page 28: Chapter 2 Motion in one dimension. s, v, a Displacement: ( m ) Where you are Velocity: ( m/s ) The rate of change of displacement Acceleration: ( m/s.](https://reader035.fdocuments.in/reader035/viewer/2022062321/56649f285503460f94c40068/html5/thumbnails/28.jpg)
Find the displacement between the following times:
Hint: Find the area.
Vel
ocity
(m
/s)
1) 0s to 5s2) 5s to 6s3) 6s to 10s4) 8s to 11s5) 2s to 8s
![Page 29: Chapter 2 Motion in one dimension. s, v, a Displacement: ( m ) Where you are Velocity: ( m/s ) The rate of change of displacement Acceleration: ( m/s.](https://reader035.fdocuments.in/reader035/viewer/2022062321/56649f285503460f94c40068/html5/thumbnails/29.jpg)
Find the displacement between the following times:
Vel
ocity
(m
/s)
1) 0s to 5s
![Page 30: Chapter 2 Motion in one dimension. s, v, a Displacement: ( m ) Where you are Velocity: ( m/s ) The rate of change of displacement Acceleration: ( m/s.](https://reader035.fdocuments.in/reader035/viewer/2022062321/56649f285503460f94c40068/html5/thumbnails/30.jpg)
Find the displacement between the following times:
Vel
ocity
(m
/s)
5s to 6s
![Page 31: Chapter 2 Motion in one dimension. s, v, a Displacement: ( m ) Where you are Velocity: ( m/s ) The rate of change of displacement Acceleration: ( m/s.](https://reader035.fdocuments.in/reader035/viewer/2022062321/56649f285503460f94c40068/html5/thumbnails/31.jpg)
Find the displacement between the following times:
Vel
ocity
(m
/s)
6s to 10s
![Page 32: Chapter 2 Motion in one dimension. s, v, a Displacement: ( m ) Where you are Velocity: ( m/s ) The rate of change of displacement Acceleration: ( m/s.](https://reader035.fdocuments.in/reader035/viewer/2022062321/56649f285503460f94c40068/html5/thumbnails/32.jpg)
Find the displacement between the following times:
Vel
ocity
(m
/s)
8s to 11s
![Page 33: Chapter 2 Motion in one dimension. s, v, a Displacement: ( m ) Where you are Velocity: ( m/s ) The rate of change of displacement Acceleration: ( m/s.](https://reader035.fdocuments.in/reader035/viewer/2022062321/56649f285503460f94c40068/html5/thumbnails/33.jpg)
Find the displacement between the following times:
Vel
ocity
(m
/s)
2s to 8s
![Page 34: Chapter 2 Motion in one dimension. s, v, a Displacement: ( m ) Where you are Velocity: ( m/s ) The rate of change of displacement Acceleration: ( m/s.](https://reader035.fdocuments.in/reader035/viewer/2022062321/56649f285503460f94c40068/html5/thumbnails/34.jpg)