Physics
• Physics is the most basic of the sciences. It is
the study of forces, motion, light, heat, sound,
energy, matter, atomic and subatomic
structure.
Kinematics
• Kinematics is the branch of physics that
describes the motion of points, bodies
(objects), and systems of bodies (groups of
objects) without consideration of the causes
of motion.
Kinematics
• Relative motion - All motion is relative. Right
now we appear to be motionless relative to
each other.
Kinematics
• If an observer from space were to look at us,
he would realize that we actually are in
motion.
Kinematics
• We are moving because we are on the earth
which is rotating.
Kinematics
• The earth is also moving around the sun. The
sun is moving through the Milky Way, and so
on.
Kinematics
• We appear to be motionless relative to each
other, because we are moving together. We
say that we are in the same frame of
reference.
Kinematics
• In this course we will be talking only about
motion of objects relative to the surface of the
earth unless otherwise stated.
Kinematics
• Speed is a measure of how fast something is
moving . It is measured in terms of a unit of
distance divided by a unit of time. Examples
are:
m
• meters per second s
mi
• miles per hour h
km
• kilometers per hour h
• The word “per” means “divided by”.
Kinematics
• Instantaneous speed is a speed at any given
instant. It is the speed read by the
speedometer in your car.
• Average speed is the total distance covered
divided by the time interval required to cover
that distance.
total distance covered
average speed =
time interval
Kinematics
• Example: You travel a distance of 100 miles
during the time interval of two hours. What is
your average speed?
total distance covered
average speed =
time interval
100mi 50mi
average speed =
=
2h
h
Kinematics
• Notice how the units follow the numbers in
the calculations.
• The units are treated like the letters in
algebra.
Kinematics
• In physics speed and velocity mean two different
things.
• Velocity means speed in a given direction.
• If we say a car is moving at we are talking
about speed. Speed is a scalar quantity. It is
characterized only by magnitude.
• If we say a car is moving at north we are
talking about velocity. Velocity is a vector
quantity. It is characterized by magnitude and
direction.
60
km
h
60
km
h
Kinematics
• In order for an object to be moving with
constant velocity its speed must be constant,
and its direction must also be constant.
• If either the speed and direction of a moving
object is changing, or if both are changing,
then it's moving with changing velocity.
Kinematics
Acceleration
• Acceleration is defined as change in velocity
per time interval
change in velocity
aceleration =
time interval
Kinematics
Acceleration
• For motion in a straight line
change in speed
aceleration =
time interval
Kinematics
Acceleration
• Units for acceleration.
 displacement 
change in velocity  time interval 
acceleration =
=

time interval
time interval
displacement
displacement

 time interval    time interval   time interval 2
Kinematics
Acceleration is a vector quantity. It is
characterized by both magnitude and direction
Kinematics
Example:
A motorcycle is traveling north at 20 m/s. Two
seconds later it's velocity is 40 m/s north. What
was its acceleration during the two seconds?
Kinematics
Solution:
 m   m  
m
change in velocity=  40    20   North  20 North
s 
s 
s

time interval= 2s
 m
 20 
m
s

acceleration=
 10 2 North
2s
s
Kinematics
Distance is a scalar measure of the interval
between two locations measured along the
actual path connecting them.
Displacement is a vector measure of the interval
between two locations measured along the
shortest path connecting them.
Kinematics
Example 1:
A person is walking east. After walking for a distance of
100 meters, the person reverses direction and walks for
a distance of 50 meters west.
1. What was the distance covered?
2. What was the person’s displacement?
3. If the trip took 90 seconds what was the average
speed?
4. If the trip took 90 seconds what was the average
velocity?
Kinematics
Example 1:
Answer:
1. The total distance was, d=100m+50m=150m
2. If we designate east as the positive direction,
than the displacement was, d=100m + (-50m)= 50m or 50m east
150m
m

1.67
3. The average speed was 90s
s
4. The average velocity was
m
 50m 
v 

0.556

s
 90 s 
Kinematics
Example 2:
A person is walking east. After walking for a
distance of 100 meters, the person reverses direction
and walks for a distance of 150 meters west.
1. What was the distance covered?
2. What was the person’s displacement?
3. If the trip took 200seconds what was the
average speed?
4. If the trip took 200 seconds what was the
average velocity?
Kinematics
Example 2:
Answer:
1. The total distance was, d=100m+150m=250m
2. If we designate east as the positive direction,
than the displacement was
d=100m + (-150m)= -50m or 50m west
m
m
 1.25
1. The average speed was v  250
200 s
s
2. The average velocity was
m
m
 50m 
v 


0.25
or
0.25
west

200
s
s
s


Kinematics
Mathematical relationships between distance
speed velocity and acceleration.
We will use the following symbols: An arrow
above a symbol indicates that it is a vector
quantity
d  distance
d  displacement
v = speed
v = velocity
a = acceleration
t = time
Kinematics
The basic relationships assuming that initial
d , d , v, and v are zero
d
v =
t
d
v =
t
a =
v
t
Kinematics
For a situation where the initial speed or the
initial velocity is equal to zero, the following
relationships hold.
vt = d
vt = d
1 2
d = at v  at
2
2d
v

a
v

average
2
t
2
Kinematics
• When an object is in free fall it means that the
only force acting on it is the force of gravity.
• On earth this means that we must ignore the
resistance of air. This is a good approximation
if an object has a small surface area, a high
density, and is not moving very fast.
• For example the approximation works well for
a dropped steel sphere, but not for a dropped
tissue.
Kinematics
Near the surface of the earth a falling object
accelerates downward with a constant
acceleration. This acceleration is equal to 9.81 sm .
m
10
Frequently we use a rounded value of s for
calculations. This acceleration is referred to as
acceleration due to gravity and is represented by
a lowercase g.
2
2
In the case of free fall instead of using
a for acceleration we use g in the
previous equations.
Kinematics
Free fall
v  gt
1 2
d = gt
2
Kinematics – free fall
Speed versus time table using g=10m/s2
Elapsed time(seconds)
Speed(meters/seco
nd)
0
0
1
10
2
20
3
30
4
40
5
50
6
60
7
70
8
80
t
v  gt
Kinematics – free fall
Speed versus time table using g=10m/s2
Speed versus time table using g=10m/s2
90
80
Speed(meters/second)
70
60
50
40
30
The slope of this
line is the
acceleration.
20
10
0
0
1
2
3
4
5
time(seconds)
6
7
8
9
Kinematics – free fall
Distance versus time table using g=10m/s2
Elapsed time(seconds)
Distance(meters)
0
0
1
5
2
20
3
45
4
80
5
125
6
180
7
245
8
320
t
1 2
gt
2
Kinematics – free fall
Distance versus time plot using g=10m/s2
350
300
Distance(meters)
250
200
150
100
50
0
0
1
2
3
4
5
Time(seconds)
6
7
8
9