Chapter 2
Kinematics in One Dinlension
2.1 !lliPlacement
The displacement is a vector that points from the object's
initial position to the object's final position and has a
magnitude that equals the shortest distance between the
two positions.
The SI unit of displacement is the meter.
+'('n\s h...
'3
If
2.2 fuJeed and Velocity
Average Speed equals the total distance traveled divided
by the time required to cover that distance. That is,
average speed ==
distance
tzme
--.--1
Go over example 1
1
Average Velocity equals the displacement of the object
divided by the time required by the object to undergo that
displacement. That is,
<v >=
-+
J),.r
J),.t
displacement
time
The instantaneous velocity vof an object indicates how
fast the object moves and the direction of the motion at
the specified instant of time. The magnitude of the
instantaneous velocity is called the instantaneous speed.
Go over example 2
2.3 Acceleration
A. Average acceleration over some time interval 8.t is
defined as the change in the velocity 8.v of an object
divided by the time 8.t. That is,
-+
J),.v
<a>=J),.t
=10 m/ sec fvi = 30 m/sec
8.t = 2.0 sec,
Ex. If Vi
Then
< a >= (30m/ sec f-) - (10m/ sec f-)
2sec
2
<a >=
--+
<a
alternatively,
-=-
l- \
0
(30m/ sec + (10m/ sec ---7)
2sec
>= (10 m/ sec2 t.l\? \ ')
-10 m/ sec 2
y
x
t =L. 2... 5ec
> -=
V:f
-v.
'"
-t:.
0
-= ) - (-1 ;:"'\
.)
_
"2..
For motion in a straight line:
(a) The object speeds up if the velocity vector points in
the same direction as the acceleration vector.
(b) The object slows down if the velocity vector points
in the opposite direction as the acceleration vector.
3
Go over example 4
2.4 of Kinematics for Constant Acceleration
The kinematics equations describing the motion of an
object moving with constant acceleration are:
_
_
_
1 _
rf - ro = vot +- a t
2
2
v-2f = v-20 + 2 a- (-rf - r-o )
2.5 AJ!plications of the Equations of Kinematics
Go over example 9
2.6 Freely Falling Bodies
A freely falling object is any object moving only under
the influence of gravity, regardless of its initial motion.
The free fall acceleration
[ a=9.8
a near the Earth's surface is
m 2 J, = 32
fi 2 J, =980
em2 J,
I
sec
sec
sec
.
Denote the magnitude of the free-fall acceleration as
g - 9.8
m
sec
2
Go over examples 12 and 13.
4
2.7 Graphical Analysis of Velocity and Acceleration
Graphical Interpretation of velocity:
See figure 2.19
Graph of position versus time for the motion of a car
moving along the x-axis.
+1200
§
+800
'"
:;:;
(
:::
I
x",+400m
0
';;;
0
+400
a..
Figure 2.19 This position-vs.-time
graph consists of three straight-line
segments, each corresponding to a
different constant velocity,
o
o
f\
Llt =
'
'200
200 s
- -- --- - - - 400
600
800
1000
1200
1400
1600
1800
Time t(s)
Average velocity is the slope of the straight line joining
the initial and the final points of the position versus time
curve.
\5
\If/I'D
-
80'0 m.-
---
--'
5
.-
ft +0
A
':::...
-,
5
7
16 .
Instantaneous Velocity
See figure 2.20
The instantaneous velocity of an object equals the slope
of the tangent line to the position versus time curve at the
instant of interest.
80.0
Tangent line
60.0
" 40.0
<:
15
c..
20.0
o
o
5.0
10.0 15.0 20.0 25.0
Time t (s)
Figure 2.20 When the velocity is
changing, the position-vs.-time graph is
a curved line. The slope I::u!!.lt of the
tangent line drawn to the curve at a
given time is the instantaneous velocity
at that time.
Instantaneous Acceleration
The instantaneous acceleration of an object equals the
slope of the tangent line to the velocity versus tin1e curve
at the instant of interest.
.5
+24
---+--+---
;:>
'g
+12 t---.......,....."'--I--="-t-'::..=.-..!------\
I
o
o
"0'" +5 m/s
I
'
123
4
5
Time t (s)
2.21 A velocity·vs.-time graph
that applies to an object with an
acceleration of Ilv/Ilt = +6 mls 2 The
initial velocity is va = +5 mls when
t 0 S.
6