linear motion
• speed and velocity
• changing velocity
• distance traveled
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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
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speed
• speed = rate of travel
• average speed = (distance traveled)/time
• “speed” assumes “time” is small
• “average speed” assumes “time” is large
(i.e., speed may vary)
• velocity = speed and direction
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Velocity
• Velocity is speed in a given direction (velocity is a vector,
speed is a scalar)
• frequently we use “+” to mean “upward” or “rightward”
and “-” to mean “leftward” or “downward”
• Note that an object may have constant speed
but changing velocity
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Displacement
• displacement = change in position
• when velocity is constant (unchanging),
the displacement = vt, where v = velocity
and t = time.
• 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
Acceleration = change of velocity SI unit: m/s/s
time interval
The motorcycle rider
experiences an
acceleration in each
case shown.
What are the
directions for each
case?
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Question
• Can an object have zero velocity but non-zero acceleration?
Answer: Yes!
Eg. Throw a ball up in the air – at the top of its flight, as it turns around it has
momentarily zero speed but is changing its direction of motion, so has non-
zero acceleration
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Free fall
• falling under influence of gravity
alone (no air resistance, etc.)
• a = “g” = 10m/s/s
• independent of mass (free-fall)
• from rest: v = gt.
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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 x t d = ½gt2.
• Example: after 3.0 seconds:
d = ½(10)(3)2 = 5x9 = 45 meters
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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 ½ s up and ½ s down.
Substituting ½ = 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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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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3 summary
• speed is the rate of travel
• velocity is speed and direction
• acceleration is the rate of change of
velocity
• for free-fall:
a = g = 10 m/s/s
v = gt
d = ½gt2.
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