lecture 2: one dimensional motion. position, distance, and displacement before describing motion,...
TRANSCRIPT
![Page 1: Lecture 2: One Dimensional Motion. Position, Distance, and Displacement Before describing motion, you must set up a coordinate system – define an origin](https://reader035.vdocument.in/reader035/viewer/2022062620/551a142b55034619378b4f6c/html5/thumbnails/1.jpg)
Lecture 2:One Dimensional Motion
![Page 2: Lecture 2: One Dimensional Motion. Position, Distance, and Displacement Before describing motion, you must set up a coordinate system – define an origin](https://reader035.vdocument.in/reader035/viewer/2022062620/551a142b55034619378b4f6c/html5/thumbnails/2.jpg)
Position, Distance, and DisplacementBefore describing motion, you must set up a coordinate system – define an origin and a positive direction.
The distance is the total length of travel; if you drive from your house to the grocery store and back, you have covered a distance of 8.6 mi. Your net displacement is zero.
![Page 3: Lecture 2: One Dimensional Motion. Position, Distance, and Displacement Before describing motion, you must set up a coordinate system – define an origin](https://reader035.vdocument.in/reader035/viewer/2022062620/551a142b55034619378b4f6c/html5/thumbnails/3.jpg)
Position, Distance, and Displacement
If you drive from your house to the grocery store and then to your friend’s house, your displacement is -2.1 mi and the distance you have traveled is 10.7 mi.
![Page 4: Lecture 2: One Dimensional Motion. Position, Distance, and Displacement Before describing motion, you must set up a coordinate system – define an origin](https://reader035.vdocument.in/reader035/viewer/2022062620/551a142b55034619378b4f6c/html5/thumbnails/4.jpg)
You and your dog go for a walk to the
park. On the way, your dog takes many
side trips to chase squirrels or examine
fire hydrants. When you arrive at the
park, do you and your dog have the
same displacement?
a) yes
b) no
Walking the Dog
![Page 5: Lecture 2: One Dimensional Motion. Position, Distance, and Displacement Before describing motion, you must set up a coordinate system – define an origin](https://reader035.vdocument.in/reader035/viewer/2022062620/551a142b55034619378b4f6c/html5/thumbnails/5.jpg)
You and your dog go for a walk to the
park. On the way, your dog takes many
side trips to chase squirrels or examine
fire hydrants. When you arrive at the
park, do you and your dog have the
same displacement?
a) yes
b) no
Yes, you have the same displacement. Because you and your dog
had
the same initial position and the same final position, then you have
(by definition) the same displacement.
Walking the Dog
Follow-up: have you and your dog traveled the same distance?
![Page 6: Lecture 2: One Dimensional Motion. Position, Distance, and Displacement Before describing motion, you must set up a coordinate system – define an origin](https://reader035.vdocument.in/reader035/viewer/2022062620/551a142b55034619378b4f6c/html5/thumbnails/6.jpg)
Average SpeedThe average speed is defined as the distance traveled divided by the time the trip took:
Average speed = distance / elapsed time
If you drive from your house to the grocery store and then to your friend’s house, your displacement is -2.1 mi and the distance you have traveled is 10.7 mi. The trip takes 30 minutes (with traffic and lights).What is your average speed?
10.7 miles
0.5 hourssav =
= 21.4 miles/hr
![Page 7: Lecture 2: One Dimensional Motion. Position, Distance, and Displacement Before describing motion, you must set up a coordinate system – define an origin](https://reader035.vdocument.in/reader035/viewer/2022062620/551a142b55034619378b4f6c/html5/thumbnails/7.jpg)
Average VelocityAverage velocity = displacement / elapsed time
If you return to your starting point, your average velocity is zero.
![Page 8: Lecture 2: One Dimensional Motion. Position, Distance, and Displacement Before describing motion, you must set up a coordinate system – define an origin](https://reader035.vdocument.in/reader035/viewer/2022062620/551a142b55034619378b4f6c/html5/thumbnails/8.jpg)
You and your dog go for a walk to the
park. On the way, your dog takes
many side trips to chase squirrels
or examine fire hydrants. When
you arrive at the park, you
affectionately pat your dog’s head.
Which statement correctly describes
your average speed and velocity
relative to that of your dog, on the
trip from home to the park?
a) Average speed and average velocity were both different
b) Average speed was the same, but average velocity was different
c) Average speed was different, but average velocity was the same
d) Average speed and average velocity were the same
Walking the Dog II
![Page 9: Lecture 2: One Dimensional Motion. Position, Distance, and Displacement Before describing motion, you must set up a coordinate system – define an origin](https://reader035.vdocument.in/reader035/viewer/2022062620/551a142b55034619378b4f6c/html5/thumbnails/9.jpg)
You and your dog go for a walk to the
park. On the way, your dog takes
many side trips to chase squirrels
or examine fire hydrants. When
you arrive at the park, you
affectionately pat your dog’s head.
Which statement correctly describes
your average speed and velocity
relative to that of your dog, on the
trip from home to the park?
a) Average speed and average velocity were both different
b) Average speed was the same, but average velocity was different
c) Average speed was different, but average velocity was the same
d) Average speed and average velocity were the same
Walking the Dog II
Your dog’s many side trips mean that he travelled more distance
than you in the same amount of time, so his average speed must
have been greater. However, his net displacement was the same
(starting and ending at the same place), so his average velocity must
have been the same.
![Page 10: Lecture 2: One Dimensional Motion. Position, Distance, and Displacement Before describing motion, you must set up a coordinate system – define an origin](https://reader035.vdocument.in/reader035/viewer/2022062620/551a142b55034619378b4f6c/html5/thumbnails/10.jpg)
Averaging Speed
Is the average speed of the red car a) 40.0 mi/h, b) more than 40.0 mi/h, or c) less than 40.0 mi/h?
Hint: is t1 = t2?
![Page 11: Lecture 2: One Dimensional Motion. Position, Distance, and Displacement Before describing motion, you must set up a coordinate system – define an origin](https://reader035.vdocument.in/reader035/viewer/2022062620/551a142b55034619378b4f6c/html5/thumbnails/11.jpg)
Position vs. Time
Consider this motion sequence, plotted here in one-dimension...
...and here as an x-t graph
average velocity
![Page 12: Lecture 2: One Dimensional Motion. Position, Distance, and Displacement Before describing motion, you must set up a coordinate system – define an origin](https://reader035.vdocument.in/reader035/viewer/2022062620/551a142b55034619378b4f6c/html5/thumbnails/12.jpg)
Instantaneous Velocity
The instantaneous velocity is tangent to the curve.
Evaluating the average velocity over a shorter and shorter period of time, one approaches the “instantaneous velocity”.
![Page 13: Lecture 2: One Dimensional Motion. Position, Distance, and Displacement Before describing motion, you must set up a coordinate system – define an origin](https://reader035.vdocument.in/reader035/viewer/2022062620/551a142b55034619378b4f6c/html5/thumbnails/13.jpg)
Graphical Interpretation of Average and Instantaneous Velocity
![Page 14: Lecture 2: One Dimensional Motion. Position, Distance, and Displacement Before describing motion, you must set up a coordinate system – define an origin](https://reader035.vdocument.in/reader035/viewer/2022062620/551a142b55034619378b4f6c/html5/thumbnails/14.jpg)
Position v. Time I
t
x
The graph of position versus
time for a car is given below.
What can you say about the
velocity of the car over time?
a) it speeds up all the time
b) it slows down all the time
c) it moves at constant velocity
d) sometimes it speeds up and
sometimes it slows down
e) not really sure
![Page 15: Lecture 2: One Dimensional Motion. Position, Distance, and Displacement Before describing motion, you must set up a coordinate system – define an origin](https://reader035.vdocument.in/reader035/viewer/2022062620/551a142b55034619378b4f6c/html5/thumbnails/15.jpg)
t
x
The graph of position versus
time for a car is given below.
What can you say about the
velocity of the car over time?
The car moves at a constant velocity
because the x vs. t plot shows a straight
line. The slope of a straight line is
constant. Remember that the slope of x
vs. t is the velocity!
a) it speeds up all the time
b) it slows down all the time
c) it moves at constant velocity
d) sometimes it speeds up and
sometimes it slows down
e) not really sure
Position v. Time I
![Page 16: Lecture 2: One Dimensional Motion. Position, Distance, and Displacement Before describing motion, you must set up a coordinate system – define an origin](https://reader035.vdocument.in/reader035/viewer/2022062620/551a142b55034619378b4f6c/html5/thumbnails/16.jpg)
t
x
a) it speeds up all the time
b) it slows down all the time
c) it moves at constant velocity
d) sometimes it speeds up and
sometimes it slows down
e) not really sure
The graph of position vs.
time for a car is given below.
What can you say about the
velocity of the car over
time?
Position v. Time II
![Page 17: Lecture 2: One Dimensional Motion. Position, Distance, and Displacement Before describing motion, you must set up a coordinate system – define an origin](https://reader035.vdocument.in/reader035/viewer/2022062620/551a142b55034619378b4f6c/html5/thumbnails/17.jpg)
a) it speeds up all the time
b) it slows down all the time
c) it moves at constant velocity
d) sometimes it speeds up and
sometimes it slows down
e) not really sure
x
The graph of position vs.
time for a car is given below.
What can you say about the
velocity of the car over
time?
The car slows down all the time because the slope of the x vs. t graph is diminishing as time goes on. Remember that the slope of x vs. t is the velocity! At large t, the value of the position x does not change, indicating that the car must be at rest.
t
Position v. Time II
![Page 18: Lecture 2: One Dimensional Motion. Position, Distance, and Displacement Before describing motion, you must set up a coordinate system – define an origin](https://reader035.vdocument.in/reader035/viewer/2022062620/551a142b55034619378b4f6c/html5/thumbnails/18.jpg)
Acceleration
Average acceleration:
Instantaneous acceleration:
![Page 19: Lecture 2: One Dimensional Motion. Position, Distance, and Displacement Before describing motion, you must set up a coordinate system – define an origin](https://reader035.vdocument.in/reader035/viewer/2022062620/551a142b55034619378b4f6c/html5/thumbnails/19.jpg)
Graphical Interpretation of Average and Instantaneous Acceleration
![Page 20: Lecture 2: One Dimensional Motion. Position, Distance, and Displacement Before describing motion, you must set up a coordinate system – define an origin](https://reader035.vdocument.in/reader035/viewer/2022062620/551a142b55034619378b4f6c/html5/thumbnails/20.jpg)
Sign of Acceleration
Speed increasingSpeed Decreasing
Does deceleration mean “negative acceleration”?
No. It means “decreasing speed”.
![Page 21: Lecture 2: One Dimensional Motion. Position, Distance, and Displacement Before describing motion, you must set up a coordinate system – define an origin](https://reader035.vdocument.in/reader035/viewer/2022062620/551a142b55034619378b4f6c/html5/thumbnails/21.jpg)
Acceleration
Acceleration (increasing speed) and deceleration (decreasing speed) should not be confused with the direction (or sign) of velocity and acceleration:
![Page 22: Lecture 2: One Dimensional Motion. Position, Distance, and Displacement Before describing motion, you must set up a coordinate system – define an origin](https://reader035.vdocument.in/reader035/viewer/2022062620/551a142b55034619378b4f6c/html5/thumbnails/22.jpg)
Graphical Interpretation of Average and Instantaneous Acceleration
![Page 23: Lecture 2: One Dimensional Motion. Position, Distance, and Displacement Before describing motion, you must set up a coordinate system – define an origin](https://reader035.vdocument.in/reader035/viewer/2022062620/551a142b55034619378b4f6c/html5/thumbnails/23.jpg)
Constant Acceleration
If the acceleration is constant, the velocity changes linearly with time:
Average velocity:
![Page 24: Lecture 2: One Dimensional Motion. Position, Distance, and Displacement Before describing motion, you must set up a coordinate system – define an origin](https://reader035.vdocument.in/reader035/viewer/2022062620/551a142b55034619378b4f6c/html5/thumbnails/24.jpg)
Propeller carv
ta:
v
tb:
v
tc:
v
td:
Which of the above
plots represents the v
vs. t graph for the
motion of the propeller
car after it was pushed?
e: Not Sure
![Page 25: Lecture 2: One Dimensional Motion. Position, Distance, and Displacement Before describing motion, you must set up a coordinate system – define an origin](https://reader035.vdocument.in/reader035/viewer/2022062620/551a142b55034619378b4f6c/html5/thumbnails/25.jpg)
Propeller carv
ta:
v
tb:
v
tc:
v
td:
Which of the above
plots represents the v
vs. t graph for the
motion of the propeller
car after it was pushed?
The car has a negative initial velocity, but a constant positive acceleration. So the plot should start at a negative value, and increase linearly with increasing time.
e: Not Sure
![Page 26: Lecture 2: One Dimensional Motion. Position, Distance, and Displacement Before describing motion, you must set up a coordinate system – define an origin](https://reader035.vdocument.in/reader035/viewer/2022062620/551a142b55034619378b4f6c/html5/thumbnails/26.jpg)
Motion with Constant AccelerationPosition as a function of time
![Page 27: Lecture 2: One Dimensional Motion. Position, Distance, and Displacement Before describing motion, you must set up a coordinate system – define an origin](https://reader035.vdocument.in/reader035/viewer/2022062620/551a142b55034619378b4f6c/html5/thumbnails/27.jpg)
Motion with Constant Acceleration
The relationship between position and time follows a characteristic curve.
My guess: a ~ 7 m/s2
![Page 28: Lecture 2: One Dimensional Motion. Position, Distance, and Displacement Before describing motion, you must set up a coordinate system – define an origin](https://reader035.vdocument.in/reader035/viewer/2022062620/551a142b55034619378b4f6c/html5/thumbnails/28.jpg)
Propeller car displacement
Which of the displayed plots represents the x vs. t graph for the motion of the propeller car after it was pushed?
x
t
![Page 29: Lecture 2: One Dimensional Motion. Position, Distance, and Displacement Before describing motion, you must set up a coordinate system – define an origin](https://reader035.vdocument.in/reader035/viewer/2022062620/551a142b55034619378b4f6c/html5/thumbnails/29.jpg)
Propeller car displacement
Which of the displayed plots represents the x vs. t graph for the motion of the propeller car after it was pushed?
The car starts at zero position, with a negative initial velocity, so the displacement is growing in the negative direction. The slope is changing linearly with time to become more positive. It should be a smooth change, go through a minimum, and then change more and more quickly with increasing timex = v0t + 1/2 at2
x
t
![Page 30: Lecture 2: One Dimensional Motion. Position, Distance, and Displacement Before describing motion, you must set up a coordinate system – define an origin](https://reader035.vdocument.in/reader035/viewer/2022062620/551a142b55034619378b4f6c/html5/thumbnails/30.jpg)
Motion with Constant AccelerationVelocity as a function of position
![Page 31: Lecture 2: One Dimensional Motion. Position, Distance, and Displacement Before describing motion, you must set up a coordinate system – define an origin](https://reader035.vdocument.in/reader035/viewer/2022062620/551a142b55034619378b4f6c/html5/thumbnails/31.jpg)
Stopping Distance
1/2 Stopping Distance
3/4 Stopping Distance
Tip for save driving: if you double your speed, what happens to your stopping distance?
v = 0.7 v0
deaccelerating with constant a, take final velocity = 0,
find (x-x0) = “stopping distance”
![Page 32: Lecture 2: One Dimensional Motion. Position, Distance, and Displacement Before describing motion, you must set up a coordinate system – define an origin](https://reader035.vdocument.in/reader035/viewer/2022062620/551a142b55034619378b4f6c/html5/thumbnails/32.jpg)
Hit the Brakes!
![Page 33: Lecture 2: One Dimensional Motion. Position, Distance, and Displacement Before describing motion, you must set up a coordinate system – define an origin](https://reader035.vdocument.in/reader035/viewer/2022062620/551a142b55034619378b4f6c/html5/thumbnails/33.jpg)
Freely Falling ObjectsFree fall from rest:
Free fall is the motion of an object subject only to the influence of gravity. The acceleration due to gravity is a constant, g.
g = 9.8 m/s2
For free falling objects, assuming your y axis is
pointing up, a = -g = -9.8 m/s2
![Page 34: Lecture 2: One Dimensional Motion. Position, Distance, and Displacement Before describing motion, you must set up a coordinate system – define an origin](https://reader035.vdocument.in/reader035/viewer/2022062620/551a142b55034619378b4f6c/html5/thumbnails/34.jpg)
a) 0.1 seconds
b) 0.2 seconds
c) 2 seconds
d) not enough information to work the problem
e) not really sure
Reaction Time
In the peculiar units used by Professor Norum, his reaction time is measured to be 20 cm. What is the corresponding reaction time, in seconds? [Use g=10 m/s2]
With v0=0 and x0 = 0, position as a function of time is:
20 cm = 0.2 m, so:
t = 0.2 seconds
![Page 35: Lecture 2: One Dimensional Motion. Position, Distance, and Displacement Before describing motion, you must set up a coordinate system – define an origin](https://reader035.vdocument.in/reader035/viewer/2022062620/551a142b55034619378b4f6c/html5/thumbnails/35.jpg)
1-D motion of a vertical projectile
![Page 36: Lecture 2: One Dimensional Motion. Position, Distance, and Displacement Before describing motion, you must set up a coordinate system – define an origin](https://reader035.vdocument.in/reader035/viewer/2022062620/551a142b55034619378b4f6c/html5/thumbnails/36.jpg)
1-D motion of a vertical projectilev
ta:
v
tb:
v
tc:
v
td:
![Page 37: Lecture 2: One Dimensional Motion. Position, Distance, and Displacement Before describing motion, you must set up a coordinate system – define an origin](https://reader035.vdocument.in/reader035/viewer/2022062620/551a142b55034619378b4f6c/html5/thumbnails/37.jpg)
- Clickers, everyday, in class.
- Assignment 1 on MasteringPhysics. Due Monday, August 29, at midnight!
- Reading, for next class (Chapter 2, 3.1-3.6)
- When you exit, please use the REAR doors!
![Page 38: Lecture 2: One Dimensional Motion. Position, Distance, and Displacement Before describing motion, you must set up a coordinate system – define an origin](https://reader035.vdocument.in/reader035/viewer/2022062620/551a142b55034619378b4f6c/html5/thumbnails/38.jpg)
![Page 39: Lecture 2: One Dimensional Motion. Position, Distance, and Displacement Before describing motion, you must set up a coordinate system – define an origin](https://reader035.vdocument.in/reader035/viewer/2022062620/551a142b55034619378b4f6c/html5/thumbnails/39.jpg)
a) 1 m
b) 1.4 m
c) 2 m
d) not enough information to solve the problem
e) not really sure
Air Track
The car undergoes constant acceleration on the tilted airtrack. Where will the velocity be twice that measured at 0.5m?
With v0=0 and x0 = 0, velocity as a function of position is:
We want v2 / v1 = 2:
x2 = 4x1 = 2 m