chapter 3 linear motion. 5.description of motion speed velocity acceleration
TRANSCRIPT
Speed
Average Speed = distance/timeUnits - m/s, ft/s, etc.
Instantaneous Speed is the speed you would read from a
speedometer
Choose Different End-Points
Time
Dis
tanc
e
Find end-points Connect with a line Find slope of the line
Example of Average Speed
• You take a trip from A to B and back to A.
• You want to average 60 mph for the round trip A to B to A.
A B2 miles
• From A to B you average 30 mph.• What is your average speed on the
return trip from B to A?
30 mph
Velocity
• Average Velocity = Displacement/time
Units - m/s, ft/s, etc.
• Instantaneous Velocity of an object is
its instantaneous speed plus the
direction it is traveling
• Velocity is a vector.
Displacement and Average Velocity
D
t
Dv
Distance traveled is the length of the path taken.
ntDisplacemeD
Average velocity =
Acceleration
• Acceleration = "change" in velocity/time
Units - m/s2, ft/s2, etc.
• Acceleration is also a vector
Vel
ocity
Time
Acceleration is the slope of a Velocity vs. Time graph.
t
va
Velocity and Acceleration
• Galileo used inclined planes to study accelerations.
• He found constant accelerations for inclines. (It was too hard to measure time for free-falls.)
• He also found that the mass of the objects didn't matter.
Relationships Between v and a for Linear Motion
t
vva 0
atvv 0
atvv 0
atv If initial velocity is zero, then
or
t
va
Example
A jogger starts at zero velocity with an acceleration of 3 ft/s2. How fast is she moving after 4 seconds?
00 v atv 2/3 sfta
st 4
)4(/3 2 ssftv
sftv /12
6. FREE FALLMotion near the surface of the earth in the absence of air resistance.
The acceleration of an object is
g = 32 ft/s2 = 9.8 m/s2
How Fast
Velocity in gravitational field (starting from rest)
v = gt = 32t English
Or v = 10t Metric
atvv 0
Distance Equation
221 gttvdd oo
do = initial distance
vo = initial velocity
g = acceleration due to gravity
Free Fall
Falling in a gravitational field:Take do and vo to be zero
(object starts from the origin at rest)
Then: d = do + vot + ½at2 becomes
d = ½gt2
d = 5t2 (Metric)
Free FallTime of Fall
(s)Velocity Acquired
(m/s) – 10tDistance Fallen
(m) – 5t2
1
2
3
4
5
10
20
30
50
40
125
80
45
20
5
Free Fall Graphs
0
5
10
15
20
25
0 0.5 1 1.5 2
Time (s)D
ispl
acem
ent (
m)
0
5
10
15
20
25
0 0.5 1 1.5 2
Time (s)
Vel
ocity
(m
/s)
0
2
4
6
8
10
12
0 0.5 1 1.5 2
Time (s)
Acc
eler
atio
n (m
/s/s
)
Ball released from rest, down positive, measure distance from point of release.
Different Assumptions
0123456
0 0.5 1 1.5 2
Time (s)D
ispla
cem
ent (m
)
-15
-10
-5
0
5
10
15
0 0.5 1 1.5 2
Time (s)
Vel
ocity
(m
/s)
-12-10
-8-6-4-20
0 0.5 1 1.5 2
Time (s)
Acc
eler
atio
n (m
/s/s
)
Ball thrown up from origin with an initial speed of 10 m/s, up is positive