I: Intro to Kinematics: Motion in
One Dimension
Honors Physics
Mr. Reid
 Particle Model
 Position Vector
 Displacement, distance
 Average Velocity, Average Speed
 Instantaneous Velocity, Instantaneous Speed
 Intro to the Derivative.
 Graphical Analysis (position vs time)
 Uniform Linear Motion
Video Clip of Oil Spill in Gulf
 http://www.youtube.com/watch?v=_2EXDmn
NPw0
Motion
 Motion is relative
 Origin
 Position is compared to an origin
 Coordinate system or a reference frame
Motion Diagram
t=0.75 sec
t=0.50 sec
t=0.25 sec
t=0 sec
Particle Model
t=0
. .
.
t=0.25s
.
t=0.50s
t=0.75s
.
Position Vectors
y=+4 m
o
x= -5m
x= 5m
Position (m)
x= 10 m
Position Vectors
o
x=10m
Position (m)
x=20m
Vectors and Scalars
 Scalars
 Magnitude (size)
 Vectors  Magnitude and Direction
Displacement (Dx): change in position.
Dx =xf - xi
Dx
o
x1=15m
Position, x (m)
x2=20m
Distance and Displacement
 Distance:
 Displacement
(Scalar)
Dx =xf - xi
(Vector)
Average Speed and Average Velocity
 Average Speed=
 Average Velocity=
Total Distance Travelled
Time
(Scalar)
Displacement = Dx
Dt
Time
(Vector)
Prob. #2.4
 A particle moves according to the equation
x=10t2 (x in meters, t in seconds).
 Find the average velocity for the time
interval from 2s to 3s.
 Ans: 50m/s
Instantaneous Speed
Instantaneous Velocity
 Instantaneous Speed

Speed at a given instant. (Time is very very small)
 Instantaneous Velocity

Velocity at a given instant. (Time is very very small)
 Instantaneous speed is the magnitude of
instantaneous velocity.
Instantaneous Velocity:
the limit of Dx as Dt approaches 0.
Dt
lim Dx
Dt 0
Dt
v=
v=
dx
dt
Instantaneous Velocity (or simply)
Velocity is the derivative of x with
respect to t.
v=
dx
dt
Instantaneous Velocity
 Instantaneous speed is the
magnitude of instantaneous
velocity.
Graphical Analysis of Motion
 Position vs Time
 Velocity vs Time
 Acceleration vs Time
Example 1: Graph of Position vs Time
Position
(m/s)
o
Time (s)
•Slope of Line= Average Velocity
•In this case does the slope also
equal the instantaneous velocity?
Uniform Linear Motion
 Motion with constant velocity
Straight line
 Same direction

Example 2: Graph of Position vs Time
Position
(m)
o
Time (s)
Instantaneous Velocity at a given time=
Slope of Tangent at that time
Example 2: Graph of Position vs Time
Position
40.0
(m)
20.0
o
Time (s)
2.0
Find the instantaneous velocity at 2sec
and the average velocity from 0 to 2sec.
Example 3: Position vs Time Graph
Position, (m)
20.0
10.0
A
o
0.5
-10.0
1.0
1.5
2.0
Time, (s)
 At what time(s) was the object at the origin?
 What is the average velocity from 0 to 1sec, 1 to
1.5 sec and 0 to 2sec?