Lecture 2
Chapter 1 and 2
Physics I
Kinematics in
One Dimension
Course website:
http://faculty.uml.edu/Andriy_Danylov/Teaching/PhysicsI
ResponseWare App instead of a clicker
PHYS.1410 Lecture 2 Danylov
Department of Physics and Applied Physics
Today we are going to discuss
basic kinematic stuff:

Distance/Displacement:
Section 1.3


Speed/Average velocity:
Instantaneous velocity:
Section 1.4
Section 2.2


Average Acceleration:
Section 1.5
Instantaneous Acceleration: Section 2.7
PHYS.1410 Lecture 2 Danylov
Department of Physics and Applied Physics
Mechanics
Motion
There are three branches of Mechanics:
 Kinematics
Motion
Forces
 Statics
Motion
Forces
 Dynamics
Motion
Forces
Kinematics describes motion of objects
we are not interested in reasons (forces) of a motion
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Kinematics
PHYS.1410 Lecture 2 Danylov
Department of Physics and Applied Physics
Frames of Reference
 Before starting solving any problem, we have to define a coordinate system (a frame of
reference) to describe position and motion of an object
 In this class, we will base problems in a Cartesian coordinate system.
We will have 1D and 2D problems
 We have freedom to choose direction of an axis.
 For 1 dimensional (1D) motion (motion in a straight line), it’s better to align the x-axis along a
motion direction.
 For falling bodies, we tend to describe position using the y-axis
Two dimensional (2D) problem
One dimensional (1D) problem
5
y-axis
origin
Negative direction
-x origin
1
Positive direction
+x
2
3
4
5
-5
5
x
-5
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x-axis
Distance vs. Displacement
PHYS.1410 Lecture 2 Danylov
Department of Physics and Applied Physics
Distance vs. Displacement
Distance (scalar):
the total path length traveled by an object
Displacement (vector):
how far an object is from its starting point
PHYS.1410 Lecture 2 Danylov
Department of Physics and Applied Physics
ConcepTest 1
Roller Coaster
What would be your displacement after a
complete roller coaster?
ConcepTest 2
Walking the Dog
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
A) yes
B) no
displacement?
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.
Follow-up: have you and your dog traveled the same distance?
ConcepTest 3
Odometer
Does the odometer in a car
A) distance
measure distance or
B) displacement
displacement?
C) both
If you go on a long trip and then return home, your odometer does not measure
zero, but it records the total miles that you traveled. That means the odometer
records distance.
Follow-up: how would you measure displacement in your car?
Distance vs. Displacement (1D)
Distance is a scalar
Displacement is a vector
– A vector has both magnitude and direction (or sign in 1-D)
Displacement = final position – initial position
Distance = 70+30 =100 m
x1
x2
20
40
60 70
Displacement =x2- x1=+40 m
PHYS.1410 Lecture 2 Danylov
Department of Physics and Applied Physics
x
Distance vs. Displacement (1D)
Distance = 20 m
Distance = 20 m
x2
xx11
x1
x2
Displacement = 30-10= + 20 m
Displacement = 10-30= -20 m
negative
PHYS.1410 Lecture 2 Danylov
Department of Physics and Applied Physics
Speed and Velocity
Even Hollywood feels that there is a difference between these two terms 
PHYS.1410 Lecture 2 Danylov
Department of Physics and Applied Physics
Average Speed and Average Velocity
Speed is a scalar
average speed 
distance travelled
time elapsed
(Speed: Distance traveled per
unit time interval)
Velocity is a vector
average velocity 
displaceme nt
time elapsed
(Velocity: Displacement of an object per
unit time interval)
PHYS.1410 Lecture 2 Danylov
Department of Physics and Applied Physics
ConcepTest 4
Speedometer
A) velocity
Does the speedometer in a car
B) speed
measure velocity or speed?
C) both
D) neither
The speedometer clearly measures speed, not velocity. Velocity is a
vector (depends on direction), but the speedometer does not care
what direction you are traveling.
Graphs: Average velocity
position (m)
20
15
x2
10
∆x
5
0
0
1
2
t1
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Department of Physics and Applied Physics
∆t
3
time (s)
x1
4
5
t2
6
Average velocity does not tell the whole story…
we also need
Instantaneous Velocity
If you watch a car’s speedometer, at any instant of time, the
speedometer tells you how fast the car is going at that instant.
PHYS.1410 Lecture 2 Danylov
Department of Physics and Applied Physics
Instantaneous velocity
position (m)
20
15
10
5
0
0
1
2
t1
Instantaneous velocity
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Department of Physics and Applied Physics
goes to 0
3
time (s)
4
5
6
Instantaneous velocity
 Graphically, instantaneous velocity is the slope of the x vs t plot
at a single point
 Mathematically, the instantaneous velocity is the derivative of
the position function
PHYS.1410 Lecture 2 Danylov
Department of Physics and Applied Physics
Finding instantaneous velocity from position
graphically
Turning point
Moves forward
Moves backward
. v1 (slow speed)
>0
v2 (max speed)
v3=0 (turning point)
v positive
Gentler slope ≡ lower velocity
Steeper slope ≡ higher velocity
0
It flies back.
v4 negative
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Department of Physics and Applied Physics
ConcepTest 5
Relay baton
Which one of the following x-vs-t graphs could be a
reasonable representation of the motion of a baton in
a relay race being passed from one runner to the next?
End of class
Finding Position from a Velocity Graph
∙
∙
∙
Let’s integrate it:
x
∙
Geometrical meaning
of an integral is an area
Initial
Total
position
displacement
The total displacement ∆s is called the “area under the velocity curve.”
(the total area enclosed between the t-axis and the velocity curve).
Example
displacement
The displacement is the shaded area
∆
v(t)
t
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Department of Physics and Applied Physics
ConcepTest
Position from velocity
Here is the velocity graph of an object
that is at the origin (x = 0 m) at t = 0 s.
At t = 4.0 s, the object’s
position is
A) 20 m
B) 16 m
C) 12 m
D) 8 m
E) 4 m
Displacement = area under the curve
Acceleration
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Acceleration
Velocity can also change with time: acceleration
change of velocity
average acceleration 
time elapsed
Instantaneous acceleration
If we are given x(t), we can find both velocity v(t) and acceleration a(t) as a
function of time
Speeding up: acceleration
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Department of Physics and Applied Physics
Slowing down: deceleration
Example 2-7: Acceleration given x(t).
A particle is moving in a straight line so
that its position is given by the relation
x = (2 m/s2)t2 + (3 m).
Calculate
(a) its average acceleration during the time
interval from t1 = 1 s to t2 = 2 s,
(b) its instantaneous acceleration as a
function of time.
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Department of Physics and Applied Physics
Thank you
See you on Wednesday
PHYS.1410 Lecture 2 Danylov
Department of Physics and Applied Physics