3 linear motion
• speed and velocity
• changing velocity, acceleration
• distance traveled
• Homework:
• RQ: 1, 4, 5, 6, 7, 8, 9, 10, 13, 15, 17, 18,
19, 20, 23.
• Problems: 2, 3, 6.
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motion
• measured with respect to Earth’s surface
unless otherwise indicated
• unit: meters/second m/s
• speed is the scalar of motion
• velocity is the vector of motion
• /
2
Speed
• Speed = rate of travel at a given moment
of time
distance traveled
avg. speed 
[m/s]
elapsed time
• Distance traveled = total length of a curved
path
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velocity, v
• v = speed & direction, “30mph due North”
• frequently, “+” means rightward and “-”
means leftward
• speed can be constant while velocity
changes…
• e.g. rounding a corner at constant speed
• /
4
displacement
• displacement = change in position
• displacement = vt, (v = constant)
• Example: velocity = -3m/s, time = 2s, the
displacement is vt = (-3m/s)(2s) = -6m,
• i.e., has moved 6 meters in leftward
direction ( - being left, + being right)/
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acceleration, a
•
•
•
•
“a” = rate of change of velocity
a = (change in velocity)/(time interval)
unit: m/s/s
Ex. car speeds uniformly from rest to
+20m/s in 10.0s
• a = (+20m/s)/(10.0s) = +2.0m/s/s
• //
6
Displacement with Changing
Speed
• displacement = vt, (v = constant)
• displacement = ½at2, (a = constant)
• Example: a = 2m/s/s,
displacement after 1, 2, 3, seconds:
• ½at2 = ½(2m/s/s)(1s)2 = 1m
• ½at2 = ½(2m/s/s)(2s)2 = 4m
• ½at2 = ½(2m/s/s)(3s)2 = 9m
• /
7
Free fall
• falling under influence of gravity
alone (no air resistance, etc.)
• a = “g” = 10m/s/s
• independent of mass
• from rest: v = gt.
• //
8
object thrown upward
• slows at a rate of g…
• then has zero velocity as it
changes its direction from up
to down.
• then falls speeding up at a
rate of g.
• equal elevations have same
speed (but opposite direction)
• //
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Free-Fall Distance
•
•
•
•
initial velocity = 0
final velocity = gt
average velocity = ½ (0 + gt) = ½gt.
distance d = (average velocity)x(time)
d = (½gt)(t)  d = ½gt2.
• Example: after 3.0 seconds:
d = ½(10)(3)2 = 5x9 = 45 meters
• //
10
Application: “Hang-time” of jumpers
Michael Jordan’s best hang-time was 0.9 s
Round this to 1 s. How high can he jump?
Use d = ½ g t2 . For 1 s hang-time, that’s 0.5s up and 0.5s down.
Substituting t = 0.5 seconds into the distance equation
d = ½ (10) (0.5)2 = 1.25 m
This is about 4 feet!
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3 summary
•
•
•
•
•
speed = rate of travel
velocity = speed and direction
acceleration = rate of change of velocity
General: v = at
d = ½at2.
for free-fall:
a = g = 10 m/s/s
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3 agenda
• lecture
• practicing physics: p8, p10
• lab: measurement of constant velocity and
constant acceleration
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Question (to think about…)
An airplane makes a straight back-and-forth
round trip, always at the same airspeed,
between two cities. If it encounters a mild
steady tailwind going, and the same steady
headwind returning, will the round trip take:
1. more
2. less
3. the same time as with no wind?
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For example:
Cities are 600 km apart, and plane’s airspeed is 300 km/h (relative to still air).
Time each way with no wind is 2 hours. Round trip time is 4 hours.
If a 100 km/h tailwind is blowing, the groundspeed is 400 km/h one way and 200
km/h the other. The times are: (600 km)/(400km/h) = 1.5 h
and: (600 km)/(200km/h) = 3.0 h
The round trip now takes 4.5 hours—longer than with no wind at all.
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