Chapter 2: Kinematics
•
2.1 Uniform Motion
•
2.2 Instantaneous Velocity
•
2.3 Finding Position from Velocity
•
2.4 Motion with Constant Acceleration
•
2.5 Free Fall
•
2.6 Motion on an Inclined Plane
•
2.7* Instantaneous Acceleration
Stop to think 2.1 P38
Stop to think 2.2 P44
Stop to think 2.3 P48
Stop to think 2.4 P54
Stop to think 2.5 P61
Example 2.3 P 40
Example 2.4 P 41
Example 2.7 P 45
Example 2.10 P 47
Example 2.14 P 53
Example 2.16 P 56
Example 2.18 P 58
Motion in one dimension
•
Determining the signs of position, velocity and acceleration
1 s
2 s
3 s
4 s
x
Origin
(x=0)
10
cm
20
cm
40
cm
70
cm
Motion along a straight line
Can be illustrated by
position

versus

time graph:
x
t(s)
1
2
3
4
Continuous
(smooth) curve
Position vs time graphs
Interpreting a position graph
1.What is the position at t =0min
2.What is the position at t =30min
3.What is the velocity at t = 20min
4.What is the velocity at t = 50min
5. What is the acceleration at t=20min
6. If this is V vs. t graph, and x = 0 km
at t = 0min. What is the position at t = 80 min
Finding velocity from position graphically
Uniform Motion
•
V(avg)= comstant
•
The position

vs

graph
is a straight line
•
Vs =
∆s/ ∆t
•
S
f
= S
i
+ Vs ∆t
Instantaneous velocity
•
Using motion diagrams and graphs
dt
ds
t
s
V
t
s
0
lim
Stop to think 2.2
Which velocity

versus

time goes with the
position
–
versus

time graph
C
Relating a velocity graph to a position graph
T
The value of the velocity at
Any time equals the slope of
The position graph
•
Using calculus to find the velocity
Ex. A particle’s position is given by the function
1.What is particle’s position at t = 2s?
x =

8+6 =

2 m
2. What is the velocity at t = 2s
V
t=2
=

3(2)
2
+3=

9 m/s
m
t
t
x
)
3
(
3
2
( 3 3)/
dx
V t m s
dt
Finding position from Velocity
tf
ti
s
i
f
dt
V
S
S
tf
and
between ti
V
curve
volocity
under the
area
s
i
f
S
S
Example 2.9
1.Where is particle’s turning point?
2.At what time does the particle reach the origin?
Motion with constant acceleration
t
V
V
t
V
a
i
f
t
a
V
V
i
f
2
)
(
2
/
1
2
)
(
2
)
(
t
a
t
V
t
V
t
a
V
t
V
V
s
i
i
i
i
f
s
a
Vi
V
a
V
V
V
V
t
V
V
s
f
i
f
i
f
i
f
2
)
(
2
)
(
2
)
(
2
2
Definition of acceleration
See page 57
If set t0=0s,
∆t = t
Example 2.13
A rocket sled accelerates at 50m/s
2
for 5.0 s. Coasts for 3.0 s, then deploys a
parachute and decelerates at 3.0m/s
2
until coming to a halt.
What is the maximum velocity of the rocket sled?
What is the total distance traveled?
The apple and feather in this photograph are falling in a vacuum
Two objects dropped from the same height will, if air resistance can be neglected
Hit the ground at the same time and with the same speed
Free Fall
downward
y
verticall
,
)
(
g
freefall
a
g = 9.8m/s
2
If we choose the y

axis to point vertically up
g
freefall
a
)
(
Example 2.16 A falling rock
A rock is released from rest at the top of 100

m

tall building.
How long does the rock take to fall to the ground, what is impact
velocity?
•
Y
0
=100m Y
1
=0m
•
V
y0
= 0 m/s t
0
= 0 s
2
0
1
2
/
1
gt
y
y
s
g
g
y
y
t
52
.
4
)
0
100
(
2
)
(
2
1
0
s
m
gt
V
V
y
y
/
3
.
44
52
.
4
8
.
9
0
1
Motion on an inclined plane
sin


g
a
s
Instantaneous Acceleration
dt
dV
t
V
a
t
0
lim
tf
ti
i
f
adt
V
V
Homework 2.50
•
A 1000Kg weather rocket is launched straight up. The rocket motor
provides a constant acceleration for 16s, then the motor stops. The
rocket altitude 20 s after launch is 5100m. You can ignore the air
resistance
a) What was the rocket’s acceleration during the first 16 s.
The rocket launched with Vo = 0, after 16 s
b) After motor stops, the acceleration is
–
g as free fall.
c) The rocket’s speed as it passes through a cloud 5100m above the ground
a
at
V
16
0
1
a
at
y
128
2
/
1
0
2
1
2
2
1
2
1
1
2
4
8
.
9
2
/
1
4
16
128
)
)
(
2
/
1
(
a
a
t
t
g
t
v
y
y
2
/
27
5100
4
.
78
192
s
m
a
a
s
m
a
t
t
g
V
V
/
392
4
8
.
9
16
)
(
1
2
1
2
Quiz questions:
Two stones are release from rest at certain height one after
the other
•
A) Will the difference in their speed
increase, decrease or stay the same
B) Will their separation distance increase,
decrease or stay the same
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