Physics 1010: The Physics
of Everyday Life
TODAY
• Velocity, Acceleration
• 1D motion under constant acceleration
• Newton’s Laws
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VOLUNTEERS WANTED!
PHET, The PHysics Educational Technology
project, is looking for students to interview
about some of their physics applets.
Volunteers will be paid $20/hr.
(There is no extra credit for this; just cash:-)
If interested please contact
Danielle.Harlow@colorado.edu
2
Help, Office and Tutorial Hours
TUTORIALS
Isidoros: 12:30-2:30 Thursday (same as office hours)
Shaun: 10:00-12:50 Monday
Joseph: ???
HELP
Mark (exams + overall): ???
Ye (Clickers): 3:00-5:00 Friday
Yin (Homework): 2:00-3:00 Monday and Friday
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Today
• Velocity, Acceleration
• Motion in one dimension under constant
acceleration
• Newton’s Laws
4
Position is a VECTOR
Positive to the right
Negative to the left
-10
0
feet
10
5
Velocity is a VECTOR
Moving to the right:
(position increases)
positive velocity.
Moving to the left:
(position decreases)
negative velocity.
-10
0
feet
10
6
POSITION AND VELOCITY
Sketch position vs. time graph and velocity vs. time graphs for
1) Car moving away from origin (motion detector) at steady velocity on left.
2) Car moving toward origin (mot. det.) at steady velocity on right.
0
AWAY
10
feet
+
time
Position
+
0
0
-
-
+
+
0
-
time
Velocity
Velocity
Position
-10
0
-
TOWARD
time
time
7
POSITION AND VELOCITY
time
Velocity
-
+
0
time
Position
+
Velocity
Position
0
time
+
-
+
0
+
-
0
time
-
time
Position
0
0
C
Velocity
+
B
time
-
-
Position
1) Car moving away
from origin (motion
detector) at steady
velocity.
(Vote on AWAY)
+
Velocity
Sketch position vs.
time graph and
velocity vs. time
graphs for
A
0
D
time
+
0
-
time
8
POSITION AND VELOCITY
+
0
time
Position
-
+
0
+
time
+
-
time
-
C
-
0
0
time
Position
Position
Velocity
0
B
time
-
+
Answer is B
time
Velocity
Position
0
+
Velocity
1) Car moving away
from origin (motion
detector) at steady
velocity.
(Vote on AWAY)
+
Velocity
Sketch position vs.
time graph and
velocity vs. time
graphs for
A
0
D
time
+
0
-
time
9
POSITION AND VELOCITY
time
Velocity
-
+
0
time
Position
+
Velocity
Position
0
time
+
-
+
0
+
-
0
time
-
time
Position
0
0
C
Velocity
+
B
time
-
-
Position
1) Car moving toward
from origin (motion
detector) at steady
velocity.
(Vote on TOWARD)
+
Velocity
Sketch position vs.
time graph and
velocity vs. time
graphs for
A
0
D
time
+
0
-
time
10
POSITION AND VELOCITY
+
0
time
Position
-
+
0
+
time
+
-
time
-
C
-
0
0
time
Position
Position
Velocity
0
B
time
-
+
Answer is C
time
Velocity
Position
0
+
Velocity
1) Car moving toward
from origin (motion
detector) at steady
velocity.
(Vote on TOWARD)
+
Velocity
Sketch position vs.
time graph and
velocity vs. time
graphs for
A
0
D
time
+
0
-
time
11
Algebraically: Velocity is change in position
divided by elapsed time
Velocity (v) = (final position) - (initial position)
(final time) - (initial time)
time = 1 second
position = 1 meter
distance
1 meter
0
time = 3 second
position = 0 meter
2s
4s
Change in Position = -1 meter
Time elapsed = 2 seconds
Velocity = -1 meter = -0.5 m/s
2 seconds
-1
12
Graphically: Velocity is the slope on the position
versus time plot
Velocity (v) = change in position
time elapsed
Slopes down: velocity is negative
Slopes up: velocity is positive
distance
1 meter
0
2s
4s
-1
13
We can get velocity graph
from position graph
Calculate velocity at t=2s
change in position
Velocity =
elapsed time
position
1 meter
0
time
2s
velocity
-1
-
Position at 3s is:
a) 1 m
b) -1 m
c) 0.5 m
d) -0.5 m
e) 0 m
Change in position is:
a) 1 m
b) -1 m
c) 0.5 m
d) -0.5 m
e) 0 m
+
0
4s
Position at 1s is:
a) 1 m
b) -1 m
c) 0.5 m
d) -0.5 m
e) 0 m
time
-0.5 m/s
Elapsed time is:
a) 1 s
b) 2 s
c) -1 s
d) -2 s
e) 0 s
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
14
We can get velocity graph
from position graph
velocity at t=0.5s
position
1 meter
0
time
2s
4s
A 0.
B 2.
C -2.
D 0.5
velocity
-1
+
0
-
time
-0.5 m/s
15
We can get velocity graph
from position graph
velocity at t=3.5s
position
1 meter
0
time
2s
velocity
-1
4s
A
B
C
D
+
0
-
time
-0.5 m/s
16
Given velocity, we can mathematically predict
position
change in position
Velocity =
elapsed time
change in position = velocity x elapsed time
Position = Starting position + change in position
Position = Starting position + velocity x time
x = xinitial + vt
FOR CONSTANT VELOCITY
To succeed in this course, the above algebra should be easy
17
What is the x
X(t) = xinitial + vt
•
•
•
•
A
B
C
D
final position
change in position
current position
none of the above
18
VELOCITY RECAP
• Velocity is a VECTOR: it has both magnitude
(length) and direction
• Velocity is the slope of the position graph
• Motion can be described both algebraically
(formula) and geometrically (graph)
• The two descriptions are equivalent, and we
can use one to produce the other
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WHAT IS THE DIFFERENCE BETWEEN
SPEED AND VELOCITY
a) Velocity is just to make you sound smarter
b) Velocity is the acceleration
c) Speed does not have direction
d) Velocity can be negative
e) C and d
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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.
21
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.
Answer is b. 1. Gives both magnitude and direction. 2. Gives only magnitude
22
IF SPEED IS CONSTANT 60mi/hr
CAN VELOCITY BE CHANGING?
YES
a) Direction can change but speed stay same
b) Going around a track
NO
c)
d)
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IF SPEED IS CONSTANT 60mi/hr
CAN VELOCITY BE CHANGING?
YES
Velocity has both magnitude (60mi/hr) AND
direction (north). If either magnitude OR
direction changes, velocity is changing.
A change in velocity implies ACCELERATION
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HOW IS ACCELERATION
SIMILAR TO VELOCITY?
a) they’re both vectors
b) Acceleration is the change in velocity
c) They both measure a change
d) thy’re both speed
e) They can both be calculated
25
Acceleration is to velocity
like
velocity is to position
• Velocity = Change in
position divided by
elapsed time
• Velocity = slope on
position graph
• Position = Initial
position + velocity x
time
• Must select which
direction is positive
• Acceleration = Change in
velocity divided by elapsed
time
• Acceleration = slope on
velocity graph
• Velocity = Initial velocity +
acceleration x time
• Must select which direction
is positive consistently
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ACCELERATION
Sketch Velocity vs. time graph and Acceleration vs. time graphs for
the car moving away from the motion detector and speeding up at a
steady rate.
Velocity
+
0
time
Acceleration
-
+
0
-
time
27
0
time
+
0
time
+
0
-
#1
time
time
+
0
time
-
C
#1
B
0
Velocity
Acceleration
Velocity
+
+
Velocity
time
Acceleration
0
Acceleration
+
A
-
Acceleration
Sketch
Velocity vs. time
graph
and Acceleration
vs. time graphs
for the car moving
away from the
motion detector
and speeding up
at a steady rate.
Velocity
ACCELERATION
+
0
D
#1
time
+
0
-
#1
time
28
ACCELERATION
Sketch Velocity vs. time graph and Acceleration vs. time graphs for
the car moving away from the motion detector and speeding up at a
steady rate.
-5
0
feet
Velocity
+
0
ANSWER IS C
time
-
Acceleration
5
Acceleration = change in velocity
time elapsed
+
0
-
time
29
ACCELERATION
Sketch Velocity vs. time graph and Acceleration vs. time graphs for
the car moving away from the motion detector and slowing down at a
v start
steady rate.
-10
0
Velocity
+
0
feet
10
time
Acceleration
-
+
0
-
time
30
+
0
time
-
0
time
+
0
-
#1
time
time
+
0
time
-
C
#1
B
0
Velocity
+
+
Velocity
time
Acceleration
0
Acceleration
Acceleration
Velocity
E: none of the above
+
A
-
Acceleration
Sketch
Velocity vs. time
graph
and Acceleration
vs. time graphs
for the car moving
away from the
motion detector
and slowing
down at a steady
rate.
Velocity
ACCELERATION
+
0
D
#1
time
+
0
-
#1
time
31
ACCELERATION
Acceleration
Velocity
Sketch Velocity vs. time graph and Acceleration vs. time graphs for
the car moving away from the motion detector and slowing down at a
v start
steady rate.
+
0
D
#1
ANSWER IS D
time
+
0
#1
time
Acceleration = change in velocity
time elapsed
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ACCELERATION
Which way is the cart’s weight pushing the cart?
Acceleration
Velocity
v start
+
0
D
#1
time
a) Left
b) Right
c) Out of the screen
-
+
0
#1
time
-
33
Newtons second law:
Force = mass x acceleration
• Car accelerates downhill because there is a
(gravitational) force pulling it downhill
(despite the fact that it’s moving uphill).
• Acceleration and force are in the same
direction (velocity and force do not have to
be in the same direction)
• The mass tells us the ratio
Answer is A, Left (same as acceleration)
34
From acceleration and velocity we can
find the position
Acceleration (a) = change in velocity
time elapsed
Velocity = Starting velocity + change in velocity
Velocity = Starting velocity + acceleration x time
vfinal = vinitial + at
Position = initial position + (average velocity) x time
vaverage = (vinitial + vfinal)/2 = (vinitial + vinitial + at)/2 = vinitial + (1/2) at
x = xinitial + vaverage t = xinitial + (vinitial + (1/2) at) t
x = xinitial + vinitial t + (1/2) at2
To succeed in this course you have to be able to do this algebra.
35
Summary
• Acceleration is
– Change in velocity divided by elapsed
time
– Slope on velocity versus time graph
• Position is related to acceleration
• Acceleration given by force (F = ma)
• Position, Velocity, Acceleration are all
VECTORS
(beware of the signs!)
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