velocity vs time

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•
I don’t remember class very well. Seemed like it went reasonably smoothly and was lots of
student engagement. Need to spend a bit more time on reading x and y values from graph and
getting slope. Maybe make them do as a clicker question.
•
Here and more later there was lots of confusion about signs of position and velocity and direction.
Need to use sign reversal feature of moving man to clarify. See comments on class#3.
Welcome to Physics 1010: The
Physics of Everyday Life
Instructors: Carl Wieman and Kathy Perkins
Missed class on Tuesday? Pick up Tuesday’s
handouts at the front of the room:
Syllabus (1st 2 pages) & Seating chart.
Please find your assigned seat.
Have a new clicker ….
Test it out - push button, find your number
No clicker? Bookstore to have more Monday. If no clicker,
today only fill in bubble sheet and turn in at end of class.
Motion
Understand motions around us …
balls, cars, bikes, people, atoms
….
But before how or why …
We need to be able to describe
motion… words, graphs, equations
Phys1010 Homepage Info (www.colorado.edu/physics/phys1010)
Clicker registration, Reading assignments, Homework assignments
To do: Reading 1.1 & 1.2 (due today)
Homework #1 is posted and due at 11:59 PM Tuesday night.
Online Surveys (2 links)
Important Notes on Homework:
Checkboxes --- Check all that are correct!
Numeric Answer --- Enter number only in box … no words or units …
Units either specified question or use selection menu.
Numeric Answer --- Either 4000 or 4.0E3. Will not recognize 4.0x10^3
m/s = meters/second (not miles/second)
Clicker Question: (don’t click yet … establish locations)
a) I have tried logging on to the homework system
b) I will try logging on this afternoon
c) I absolutely promise to logon on Friday.
d) none of the above
USERNAME  first initial followed by last name …. kperkins
PASSWORD  last 4 digits of ID.
Office Hours & Problem Solving Sessions
G2B87
cw
kp
Phys help
room
Enter through
G2B90
Special Session
Next Tuesday
3-5:30 pm
Phys1010 problem solving session
in G2B87 or near by. Just look around.
Regular Weekly Hours
(Starts this Thurs.)
Wednesdays: 4-5 pm
Thursdays: 2-5 pm TODAY
Fridays: 10am-12pm
and 1-5:30pm
With Carl, Kathy, Zach,
Dan, Stephanie, and Jeff.
Homework too hard to do alone, but
ok & learn lot when work together.
We will help interactions, coach,
NOT give answers.
Reading quiz. chapters 1.1 and 1.2 (read before class, learn more)
1. The physics topic that is the primary focus of chap. 1.2 is
a) the theory of gravity
b) how air resistance affects falling objects
c) the motion of dropped or thrown objects
d) the relationship between English and metric units of mass
e) the physics behind how baseball pitchers can throw curve balls
2) If you push on two bowling balls with the same force, but one has
half the mass of the other, then … ?
a. both masses accelerate the same
b. the low mass ball accelerates faster than the high mass ball.
c. the high mass ball accelerates faster than the low mass ball.
d. none of the above.
3) If the two bowling balls fell off a table at the same time:
a) Both would fall with the same constant velocity all the way to floor.
b) The heavy ball would accelerate more rapidly.
c) The light ball would accelerate more rapidly.
d) Both would fall with the same acceleration.
Do the experiment: about how fast was Prof.
Bohn walking? (pick the closest balue)
a)
b)
c)
d)
e)
100 m/s
10 m/s
1 m/s
0.1 m/s
0 m/s
Human Motion
Velocity
+
0
-
time
Velocity
Demo 2:
Sketch velocity vs. time graph for
1) Person moving away from origin (motion detector) at steady velocity on left.
2) Person moving toward origin (mot. det.) at steady velocity on right.
+
0
time
away
toward
Human Motion
Demo 2:
Sketch velocity vs. time graph for
1) Person moving away from origin
(motion detector) at steady velocity on left.
2) Person moving toward origin
(mot. det.) at steady velocity on right.
-
-
Velocity
-
0
time
-
0
time
D
+
time
0
-
time
-
-
+
Velocity
C
+
0
time
Velocity
time
0
+
+
Velocity
0
Velocity
0
B
+
Velocity
Velocity
+
+
Velocity
A
0
time
-
time
Human Motion
Demo 2:
Sketch velocity vs. time graph for
1) Person moving away from origin (motion detector) at steady velocity on left.
2) Person moving toward origin (mot. det.) at steady velocity on right.
Velocity is a vector.
Magnitude (length) gives speed.
Pointing direction gives sign.
(positive or negative)
-10
0
10
feet
+
0
time
Velocity
Velocity
+
0
time
-
away
toward
Human Motion
Demo 2:
Sketch velocity vs. time graph for
1) Person moving away from origin (motion detector) at steady velocity on left.
2) Person moving toward origin (mot. det.) at steady velocity on right.
Velocity is a vector.
Magnitude (length) gives speed.
Pointing direction gives sign.
(positive or negative)
-10
0
10
feet
+
0
-
time
Velocity
Velocity
+
0
-
time
What is the difference between “speed” and “velocity”?
1. You are driving 60 miles per hour north.
2. You are driving 60 miles per hour.
a. both give your speed, can’t tell your velocity.
b. 2. gives speed, 1. gives velocity.
c. both are giving your velocity.
d. 2 gives velocity, 1. gives your speed.
ans. b. 1. gives speed and direction = velocity. 2. gives only your
speed, but since direction not specified, do not know velocity.
if speed is constant 60 mph, can velocity be changing?
yes! driving in circle. direction changing = velocity changing
= accelerating!
Human Motion
Demo 3:
Sketch position vs. time and velocity vs. time graphs for person moving
away from origin (motion detector) at twice velocity of Demo #1 and 2.
Position
+
0
#1
time
Describe in words how
the velocity vs time and
position vs time graphs
change when the speed
is twice as fast.
Velocity
+
#1
0
-
time
Human Motion
A
0
time
-
+
#1
time
0
+
Position
#1
Velocity
Velocity
Position
+
+
time
+
-
#1
time
0
#1
time
+
Position
#1
-
0
time
D
Velocity
Position
0
#1
0
C
+
B
-
-
Velocity
Demo 3:
Sketch position vs.
time and velocity vs.
time graphs for person
moving away from
origin (motion detector)
at twice velocity of
Demo #1 and 2.
0
#1
time
+
0
-
#1
time
Human Motion
Demo 3:
Sketch position vs. time and velocity vs. time graphs for person moving
away from origin (motion detector) at twice velocity of Demo #1 and 2.
velocity
Position
+
0
D
#1
time
Describe in words how
the velocity vs time and
position vs time graphs
change when the speed
is twice as fast.
Velocity
+
#1
0
-
time
How does position (distance) vs time relate to velocity vs time?
Velocity graph is slope of position graph.
1 meter
What does
velocity graph
look like?
2s
time
4s
-1
velocity
Velocity at 2 s is:
a) 1 m/s
b) -1 m/s
c) 0.5 m/s
d) -0.5 m/s
e) - 1/6 m/s
0
+
0
-0.5 m/s
man walking, with cursors, web demo.
+0.25 m/s
time
Equations also help us describe and think about motion
Velocity (v) = change in position = distance traveled
time elapsed
time it took
Position = Starting position + change in position
Position = Starting position + velocity x time
x = xinitial + vt
time = 1 second
position = 1 meter
V is slope of
position vs time
graph
How do you know direction?
time = 3 second
position = 0 meter
1 meter
Change in Position = -1 meter
0
-1
2s
4 s Time elapsed = 2 seconds
Velocity = -1 meter = -0.5 m/s
2 seconds
Equations also help us describe and think about motion
What if velocity is changing? … Accelerating
Acceleration (a) = change in velocity
time elapsed
A is slope
of velocity vs time graph
Velocity = Starting velocity + change in velocity
Velocity = Starting velocity + acceleration x time
v = vinitial + at
=vinitial + ½(change in velocity)
And now
=vinitial + ½at
Position = initial position + (average velocity) x time
x = xinitial + vinitial t + ½ at2
And
Distance traveled = (average velocity) x time = vinitial t + ½ at2
Check with moving man graphs, or cart data to see if true.
Do yours as dashed line,
compare with team members
then make solid line based
on group.
Position
+
0
time
-
Velocity
Demo 4:
Sketch position vs time and
velocity vs time graphs for
when Moving Man:
walks steadily towards the
tree for 6 seconds,
then stands still for 6
seconds, and
then towards the house twice
as fast as before for 6
seconds.
+
0
time
5s
10 s
15 s
20 s
0
time
Position
Position
+
A
Position
time
5s
10 s
15 s
20 s
+ C
0
Velocity
0
time
Position
Velocity
+
time
+
0
-
time
5s
10 s
15 s
20 s
+ D
0
time
-
+
0
time
5s
10 s
15 s
Velocity
Velocity
-
-
0
-
-
-
+
B
20 s
+
0
-
time
5s
10 s
15 s
20 s
Do yours as dashed line,
compare with team members
then make solid line based
on group.
Position
+
D
0
time
+
Velocity
Demo 4:
Sketch position vs time and
velocity vs time graphs for
when Moving Man:
walks steadily towards the
tree for 6 seconds,
then stands still for 6
seconds, and
then towards the house twice
as fast as before.
0
time
5s
10 s
15 s
20 s
0 meters
-10
10
Choose to define positive direction
as towards house.
0 meters
10
-10
Choose to define positive direction
as towards tree.
Sketch graphs for
Moving Man walks from the house to the tree:
Position
0
time
Position
+
+
0
-
+
0
time
Velocity
-
Velocity
time
+
0
time
-
5s
10 s
15 s
20 s
5s
10 s
15 s
20
case a. positive towards house. case b. positive towards tree.
How do the graphs in these 2 cases compare?
a. The position vs time graphs are different; the velocity vs.
time graphs are the same.
b. Both the position vs. time and velocity vs. time graphs are
different.
c. Both the position vs. time and velocity vs. time graphs are
the same.
d. The position vs time graphs are the same. The velocity vs.
time graphs are different.
e. I can’t make sense of these graphs.
0 meters
-10
10
Choose to define positive direction
as towards house.
0 meters
10
-10
Choose to define positive direction
as towards tree.
Sketch graphs for
Moving Man walks from the house to the tree:
Position
0
time
Position
+
+
0
-
-
notice slopes and velocities
+
0
time
Velocity
Velocity
time
+
0
time
-
5s
10 s
15 s
20 s
5s
10 s
15 s
20
Human Motion
Part 1:
Walk this way & take data
Part 2:
Position
+
0
-
time
Velocity
Walk this way
& take data
+
0
-
time
How do the graphs in these 2 cases compare?
a. The position vs time graphs are different; the velocity vs.
time graphs are the same.
b. Both the position vs. time and velocity vs. time graphs are
different.
c. Both the position vs. time and velocity vs. time graphs are
the same.
d. The position vs time graphs are the same. The velocity vs.
time graphs are different.
e. I can’t make sense of these graphs.
Human Motion
Part 1:
Walk this way & take data
-10
0
10
feet
Part 2:
Walk this way,
& take data
Position
+
0
-
time
Velocity
10
+
0
-
0
feet
time
Other class rules (in addition to stuff in syllabus):
1) Turn off cell phones.
2) 1 hour and 15 minute class. (does not end at 12 or 12:05!!)
Position
Human Motion
Demo 4:
Sketch position vs time and velocity vs time graphs for when moving man
- walks steadily towards the tree for 6 seconds
- then stands still for 6 seconds, and
- then towards the house twice as fast as before.
Do yours as dashed line, compare with team members then make solid line
based on group.
+
0
time
Velocity
+
0
time
5s
10 s
15 s
20 s
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