Chapter 4 Linear Motion
Chapter 4 Linear Motion
Chapter 4 Linear Motion
Motion is Relative
Even things that appear to be at rest
move!
Identify your frame of reference.
Describe the motion of your table.
State the motion of an object with
respect to your chosen frame of
reference.
What is a Rate?
Any physical quantity divided by time
Speed =
Velocity =
Acceleration =
Distance
Time
Displacement
Time
Change in Velocity
Time
Displacement
Distance and
displacement are
NOT the same
Refers to change in
position or distance
from a starting point
A vector quantity
requires direction
Independent of path
Conceptual Physics Chapter 4
Speed
Measures how fast something is moving
The rate at which distance is covered
Scalar quantity
Typically measured in meters per second
(m/s)
Speed =
Distance
Time
d
or s =
t
Velocity
Measures how fast something is moving
AND IN WHAT DIRECTION
The rate of change in position
Vector quantity
Typically measured in meters per second
(m/s)
Displacement
x
Velocity =
or v =
Time
t
Conceptual Physics Chapter 4
Instantaneous Speed
Typically, the motion of a body will not
remain perfectly constant
d use to find the
What
tools
could
we
We can use s =
to find the average
t of an automobile?
instantaneous
speed
speed
The average speed does NOT indicate
the maximum speed, the minimum speed,
or the speed at any given instant!
Instantaneous speed cannot be
calculated in simple mathematical terms
Conceptual Physics Chapter 4
Constant Velocity
Speed remains constant
What three controls in a car allow us
Body travels in a straight line
to change velocity?
Speeding up, slowing down, and changing
direction each indicate a change in
velocity
Acceleration
Rate of change of velocity
Measures how quickly the motion of a
body changes
Vector quantity
Typically measured in meters per second
per second (m/s2)
Change in Velocity
v
Acceleration =
or a =
Time
t
Conceptual Physics Chapter 4
10
Acceleration
If an object speeds up OR slows down
OR changes direction, it undergoes an
acceleration.
11
Acceleration
In 5 seconds a car moving in a straight
line to the north increases its speed
from 50 km/hr to 75 km/hr. What is
the magnitude of its acceleration?
75 km/hr - 50 km/hr
v
=
= 5 km/hr/s
a=
5s
t
Conceptual Physics Chapter 4
12
Acceleration
What is the acceleration of a sports
car traveling on a straight roadway at
100 km/hr to the east?
Acceleration and velocity
are NOT the same!
13
Acceleration
Car A
Car B
v1 = 20 km/hr, N
v2 = 50 km/hr, N
v1 = 40 km/hr, W
v2 = 60 km/hr, W
14
Free Fall
Falling
A
golf ball
bodies
fallsspeed
to the
up ground.
as a result of
gravity.
Does
it accelerate?
If a body falls only under the influence
of gravity, it is said to be in free fall.
By definition, air resistance plays no
role in free fall.
All bodies in free fall, regardless of
mass, will accelerate at the same rate.
Conceptual Physics Chapter 4
15
Free Fall
The acceleration of a freely falling body
is denoted by g.
g = 9.8 m/s2
or approximately 10 m/s2
The direction of free-fall acceleration
is DOWNWARD this is generally
indicated with a negative sign.
Conceptual Physics Chapter 4
16
Air Resistance
How does air resistance affect
the motion of a falling body?
17
Time
0 s
1 s
2 s
3 sign
s
Negative
indicates
4 s
direction
5 s
Velocity
0 m/s
-10 m/s
-20 m/s
-30 m/s
-40 m/s
-50 m/s
What
How are
is the
v and
velocity
t related?
atv t= =gt12 s?
18
a =
Time
0
1
2
3
4
5
s
s
s
s
s
s
-40 m/s
(-30 m/s)
-10 m/s
4 s1 s 3 s
Conceptual Physics Chapter 4
Velocity
0 m/s
-10 m/s
-20 m/s
-30 m/s
-40 m/s
-50 m/s
= -10 m/s2
19
a =
Time
0
1
2
3
4
5
s
s
s
s
s
s
-50 m/s
(-20 m/s)
-30 m/s
5 s3 s 2 s
Conceptual Physics Chapter 4
Velocity
0 m/s
-10 m/s
-20 m/s
-30 m/s
-40 m/s
-50 m/s
= -10 m/s2
20
Free Fall
What
Determine
happens
the
when
acceleration
an object is
thrown
betweendownward
t = 2 s
at
and20
t =
m/s?
4 s.
Time
0 s
1 s
2 s
3 s
v = gt = (-10
+ m/s2)1= s-30
= -10
m/s m/s
4 s
This gets added to the initial
5 velocity
s
a =
-60 m/s
(-40 m/s)
-20 m/s
4 s2 s 2 s
Conceptual Physics Chapter 4
Velocity
-20 m/s
-40
-50
-60
-70
m/s
m/s
m/s
m/s
= -10 m/s2
21
Free Fall
What
Determine
happens
the
when
acceleration
an object is
thrown
betweenupward
t = 0 at
s
20
andm/s?
t = 2 s.
Time
Velocity
0 s
20 m/s
1 s
2 s
0 m/s
3 s
-10 m/s
v = gt = (-10
+ m/s2)1= s10= m/s
-10 m/s
4 s
-20 m/s
This gets added to the initial
5 velocity
s
-30 m/s
a =
0 m/s
20 m/s
-20 m/s
2 s2 s 0 s
= -10 m/s2
22
Free Fall
Determine the
acceleration
between t = 2 s
and t = 4 s.
a =
Time
0
1
2
3
4
5
s
s
s
s
s
s
-20 -20
m/s m/s
0 m/s
4 s2 s2 s
Velocity
20 m/s
10 m/s
0 m/s
-10 m/s
-20 m/s
-30 m/s
= -10 m/s2
23
Free Fall
Determine the
acceleration
between t = 0 s
and t = 5 s.
a =
Time
0
1
2
3
4
5
s
s
s
s
s
s
-30 -50
m/s m/s
20 m/s
5 s5 s0 s
Velocity
20 m/s
10 m/s
0 m/s
-10 m/s
-20 m/s
-30 m/s
= -10 m/s2
24
Free Fall
The acceleration of a body in free fall is
always, always, always
-10 m/s2
25
Free Fall
Velocity
Position
Time
A freely
falling body
released from rest
0 s be falling
0 m/s at 100m/s
m at the end of
will
1 s
-10 m/s
the first second, but HOW FAR does it
2 s
-20 m/s
fall
3 s in the
-30 first
m/s second?
v1 + v2
4 s
-40 m/s
=
5 s
-50 m/s
2
x
v =
t
x = v t
Conceptual Physics Chapter 4
26
Free Fall
Time
0
1
2
3
4
5
x =
Velocity Position
s
s
s
s
s
s
0 m/s
-10 m/s
-20 m/s
-30 m/s
-40 m/s
-50 m/s
v1 + v2
2
0 m
0 m/s
-10+ m/s
(-10 m/s)
1 s = -5 m
t =
2
Conceptual Physics Chapter 4
27
Free Fall
Time
0
1
2
3
4
5
x =
Velocity Position
s
s
s
s
s
s
0 m/s
-10 m/s
-20 m/s
-30 m/s
-40 m/s
-50 m/s
v1 + v2
2
0 m
-5 m
0 m/s
-20+ m/s
(-20 m/s)
2 s = -20 m
t =
2
Conceptual Physics Chapter 4
28
Free Fall
Time
0
1
2
3
4
5
x =
Velocity Position
s
s
s
s
s
s
0 m/s
-10 m/s
-20 m/s
-30 m/s
-40 m/s
-50 m/s
v1 + v2
2
0 m
-5 m
-20 m
0 m/s
-30+ m/s
(-30 m/s)
3 s = -45 m
t =
2
Conceptual Physics Chapter 4
29
Free Fall
Time
0
1
2
3
4
5
x =
Velocity Position
s
s
s
s
s
s
0 m/s
-10 m/s
-20 m/s
-30 m/s
-40 m/s
-50 m/s
v1 + v2
2
0 m
-5 m
-20 m
-45 m
0 m/s
-40+ m/s
(-40 m/s)
4 s = -80 m
t =
2
Conceptual Physics Chapter 4
30
Free Fall
Time
0
1
2
3
4
5
x =
Velocity Position
s
s
s
s
s
s
0 m/s
-10 m/s
-20 m/s
-30 m/s
-40 m/s
-50 m/s
v1 + v2
2
0 m
-5 m
-20 m
-45 m
-80 m
0 m/s
-50+ m/s
(-50 m/s)
5 s = -125 m
t =
2
Conceptual Physics Chapter 4
31
Free Fall
Time
0
1
2
3
4
5
x =
Velocity Position
s
s
s
s
s
s
0 m/s
-10 m/s
-20 m/s
-30 m/s
-40 m/s
-50 m/s
v1 + v2
2
0 m
-5 m
-20 m
-45 m
-80 m
-125 m
-20 m/s
-70+ m/s
(-50 m/s)
3 s = -105 m
t =
2
Conceptual Physics Chapter 4
32
Free Fall
Time
Velocity
s
s
s
s
33
Free Fall
Time
0
1
2
3
4
5
6
s
s
s
s
s
s
s
Velocity
10 m/s
0 m/s
34
Free Fall
Time
0
1
2
3
4
5
6
s
s
s
s
s
s
s
Velocity
10 m/s
0 m/s
-10 m/s
-20 m/s
-30 m/s
-40 m/s
-50 m/s
v = gt + v0
Conceptual Physics Chapter 4
35
Free Fall
Time
0
1
2
3
4
5
6
x =
s
s
s
s
s
s
s
v1 +
Velocity Position
10 m/s
0 m
0 m/s
-10 m/s
-20 m/s
-30 m/s
-40 m/s
-50 m/s
v2
10 m/s
10 m/s
+ 0 m/s
1 s = 5 m
t =
2
2
Conceptual Physics Chapter 4
36
Free Fall
Time
0
1
2
3
4
5
6
x =
s
s
s
s
s
s
s
v1 +
Velocity Position
10 m/s
0 m
0 m/s
5 m
-10 m/s
-20 m/s
-30 m/s
-40 m/s
-50 m/s
v2
10 m/s 0+ m/s
(-10 m/s)
2 s = 0 m
t =
2
2
Conceptual Physics Chapter 4
37
Free Fall
Time
0
1
2
3
4
5
6
x =
s
s
s
s
s
s
s
v1 +
Velocity Position
10 m/s
0 m
0 m/s
5 m
-10 m/s
0 m
-20 m/s
-30 m/s
-40 m/s
-50 m/s
v2
m/s m/s)
10 m/s-10
+ (-20
3 s = -15 m
t =
2
2
Conceptual Physics Chapter 4
38
Free Fall
Time
0
1
2
3
4
5
6
x =
s
s
s
s
s
s
s
v1 +
Velocity Position
10 m/s
0 m
0 m/s
5 m
-10 m/s
0 m
-20 m/s
-15 m
-30 m/s
-40 m/s
-50 m/s
v2
m/s m/s)
10 m/s-20
+ (-30
4 s = -40 m
t =
2
2
Conceptual Physics Chapter 4
39
Free Fall
Time
0
1
2
3
4
5
6
x =
s
s
s
s
s
s
s
v1 +
Velocity Position
10 m/s
0 m
0 m/s
5 m
-10 m/s
0 m
-20 m/s
-15 m
-30 m/s
-40 m
-40 m/s
-50 m/s
v2
m/s m/s)
10 m/s-30
+ (-40
5 s = -75 m
t =
2
2
Conceptual Physics Chapter 4
40
Free Fall
Time
0
1
2
3
4
5
6
x =
s
s
s
s
s
s
s
v1 +
2
Velocity Position
10 m/s
0 m/s
-10 m/s
-20 m/s
-30 m/s
-40 m/s
-50 m/s
v2
10
t =
0 m
5 m
0 m
-15 m
-40 m
-75 m
m/s m/s)
m/s-40
+ (-50
6 s = -120 m
2
41
Free Fall
Time
0
1
2
3
4
5
6
x =
s
s
s
s
s
s
s
v1 +
2
Velocity Position
10 m/s
0 m/s
-10 m/s
-20 m/s
-30 m/s
-40 m/s
-50 m/s
v2
0
t =
0 m
5 m
0 m
-15 m
-40 m
-75 m
-120 m
m/s
-40
+ (-40
m/s
2
m/s)
4 s = -80 m
42