3 linear motion

1
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.

2
motion

• measured with respect to Earths surface unless
  otherwise indicated
• unit meters/second m/s
• speed is the scalar of motion
• velocity is the vector of motion
• /

3
Speed

• Speed rate of travel at a given moment of time
• Distance traveled total length of a curved path

4
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
• /

5
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)/

6
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
• //

7
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
• /

8
Free fall

• falling under influence of gravity alone (no air
  resistance, etc.)
• a g 10m/s/s
• independent of mass
• from rest v gt.
• //

9
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)
• //

10
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 secondsd ½(10)(3)2 5x9
  45 meters
• //

11
Application Hang-time of jumpers

• Michael Jordans 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, thats 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)
15
For example Cities are 600 km apart, and
planes 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 hourslonger than with no wind at all.