Physics 221 Chapter 2

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Physics 221Chapter 2
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Speed

• Speed Distance / Time
• v d/t

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Problem 1 . . . Average Speed

• You drive from city A to city B(50 miles) at an
  average speed of 50 m.p.h. and from city B to
  city C (140 miles) at an average speed of 70
  m.p.h. What is your average speed?
• A. 50 m.p.h.
• B. 60 m.p.h.
• C. 63.3 m.p.h.
• D. 70 m.p.h

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Solution 1 . . . Average Speed

• You drive from city A to city B(50 miles) at an
  average speed of 50 m.p.h. and from city B to
  city C (140 miles) at an average speed of 70
  m.p.h. What is your average speed?
• A. 50 m.p.h.
• B. 60 m.p.h.
• C. 63.3 m.p.h.
• D. 70 m.p.h

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Speed and Velocity

• Velocity is speed in a specified direction
• Car A going at 30 m.p.h. EAST and car B going at
  30 m.p.h. NORTH have the same speed but different
  velocities!
• A car going around a circular track at 30 m.p.h.
  has a CONSTANT SPEED but its VELOCITY is CHANGING!

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Problem 2 . . . Speed and Velocity

• John Denver negotiates his rusty (but trusty)
  truck around a bend in a country road in West
  Virginia.
• A. His speed is constant but his velocity is
  changing
• B. His velocity is constant but his speed is
  changing
• C. Both his speed and velocity are changing
• D. His velocity is definitely changing but his
  speed may or may not be changing

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Solution 2 . . . Speed and Velocity

• John Denver negotiates his rusty (but trusty)
  truck around a bend in a country road in West
  Virginia.
• A. His speed is constant but his velocity is
  changing
• B. His velocity is constant but his speed is
  changing
• C. Both his speed and velocity are changing
• D. His velocity is definitely changing but his
  speed may or may not be changing

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Instantaneous Velocity

• Instantaneous means measured at a given instant
  or moment (Kodak moment). Experimentally, this
  is virtually impossible. One must measure the
  distance over an extremely short time interval
• Average means measured over an extended time
  interval. This is easier to measure.

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Distance and Displacement

• Displacement measures how far an object is from
  the starting point.
• Distance and Displacement can be very different
  if the object does not proceed in the same
  direction in a straight line!

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Problem 3 . . . On the road again!

• A car travels East from point A to point B (3
  miles) and then North from point B to point C (4
  miles).
• (a) What distance did the car travel?
• (b) What is the cars displacement?

C
A
B
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Solution 3 . . . On the road again!

• A car travels East from point A to point B (3
  miles) and then North from point B to point C (4
  miles).
• (a) Distance traveled is 7 miles
• (b) Displacement is 5 miles(NE?)

C
A
B
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Speed and Velocity . . . revisited!

• Speed distance / time
• Velocity displacement / time
• For translational motion (straight line) in the
  same direction, speed equals velocity!
• Remember to specify the magnitude and the
  direction for displacement and velocity. These
  are VECTOR quantities

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x 3 t 2

• The position of a particle moving along a
  straight line is given by the equation
• x 3 t2
• A. What is the position of the particle when t
  5 s ?
• B. What is the speed of the particle when t 5
  s?

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x 3 t 2

• A. the position of the particle when t 5 s is
  75 m
• B. The speed of the particle is
• v dx/dt
• v 6 t
• v 30 m/s
• Note Average speed is 15 m/s but instantaneous
  speed at t5s is 30 m/s

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Acceleration

• Acceleration is the rate of change of velocity
• a ( vf - vi ) / t

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Problem 4 . . . Translational Motion

• Q. Is the speed constant at t10s?
• Q. When is the acceleration zero?
• Q. When is it slowing down (decelerating)?
• Q. What is the acceleration at t7s?

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Solution 4 . . . Translational Motion

• Q. Is the speed constant at t10s? N0!
• Q. When is the acceleration zero?15s, 20s, etc.
• Q. When is it slowing down (decelerating)?45s,50s
  etc.
• Q. What is the acceleration at t7s? 1 m/s2

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Problem 5 . . . Car on a straight road

• The speed at t0 s is vi 0
• At t6 s, vf 18 m/s
• (a) Calculate d
• (b) Calculate a and v at 4s

speed
time
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Solution 5a

• Distance Area under v vs. t graph
• Area of a rectangle base x height
• Area of a triangle 1/2 x base x height
• d 1/2 x (Vf - Vi) x t
• d 54 m

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Solution 5b

• a (Vf - Vi ) / t
• a 3 m/s2
• Vf Vi a t
• Vf 0 3x4
• Vf at 4s 12 m/s

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Problem 6

• Car accelerating on a straight road
• Given Vi 2 m/s and a 3 m/s/sCalculate Vf
  when t 8s
• Draw the speed vs. time graph
• Calculate d when t 8s

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Solution 6

• Vf Vi a t
• Vf 26 m/s
• d Area rectangle triangle
• d Vi t 1/2 a t2
• d (2)(8) 1/2 (3) (64)
• d 112 m

speed
time
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Equation Summary for uniform acceleration (No
Jerks Pleeeease!)

• Vf Vi a t
• d Vi t 1/2 a t2
• Vf2 Vi2 2ad
• Vave (Vf Vi) / 2

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Problem 7

• A car accelerates from a stop light and attains a
  speed of 24 m/s after traveling a distance of 72
  m. What is the acceleration of the car?

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Solution 7

• The equation that comes to our rescue is
• Vf 2 Vi 2 2ad
• (24 )2 (0)2 2a(72)
• a 4 m/s2

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Problem 8 . . . Free Fall

• Acceleration due to gravity is 9.8 m/s2 (sea
  level on Earth)
• (a) A cat falls off a ledge. How fast is it
  moving 3 seconds after the fall?
• (b) What is the distance traveled by the
  unfortunate cat?

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Solution 8 . . . Free fall

• Vf Vi a t
• (a) Vf 0 (9.8)(3)
• Vf 29.4 m/s
• (b) d Vi t 1/2 a t2
• d 0 (1/2)(9.8)(9)
• d 44 .1 m

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Problem 9 . . . Apple tree

• Big apple is twice as big as Little apple. Both
  fall from the same height at the same time.
  Which statement is correct?
• A. Big and Little reach the ground at about the
  same time but Big is moving a lot faster
• B. Big reaches the ground a lot sooner
• C. Little reaches the ground way before Big does
• D. Big and Little reach the ground at about the
  same time but Big is moving a lot slower
• E. Big and Little reach the ground at about the
  same time and they are moving at about the same
  speed

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Solution 9 . . . Apple tree

• Big apple is twice as big as Little apple. Both
  fall from the same height at the same time.
  Which statement is correct?
• A. Big and Little reach the ground at about the
  same time but Big is moving a lot faster
• B. Big reaches the ground a lot sooner
• C. Little reaches the ground way before Big does
• D. Big and Little reach the ground at about the
  same time but Big is moving a lot slower
• E. Big and Little reach the ground at about the
  same time and they are moving at about the same
  speed

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Problem 10 . . . Grannys Orchard

• Big apple is twice as high as Little apple. They
  both fall at the same time. Let VB and VL denote
  their respective speeds just before hitting the
  ground. VB / VL is most nearly
• A. 1/2
• B. 1
• C. 1.5
• D. 2
• E. 4

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Solution 10 . . . Grannys Orchard

• Big apple is twice as high as Little apple. They
  both fall at the same time. Let VB and VL denote
  their respective speeds just before hitting the
  ground. VB / VL is most nearly
• A. 1/2
• B. 1
• C. 1.5
• D. 2
• E. 4

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Problem 11 . . . Tippity-Top

• A stone is thrown straight up with a speed of 20
  m/s.
• A. What is the speed at the tippity-top?
• B. What is the acceleration at the tippity-top?
• C. What is the time for the round trip?
• D. What is the total round trip distance?

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Solution 11 . . . Tippity-Top

• A stone is thrown straight up with a speed of 20
  m/s.
• A. What is the speed at the tippity-top? 0 m/s
• B. What is the acceleration at the tippity-top?
  g?
• C. What is the time for the round trip? 4 s
• D. What is the total round trip distance? 40 m

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• Thats all Folks!