Physics 103: Lecture 3 Position

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Physics 103 Lecture 3Position Velocity with
constant Acceleration

• Todays lecture will be on kinematic equations
• 1-d motion with constant acceleration
• free-fall

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Summary of Concepts (from last lecture)

• kinematics A description of motion
• position coordinates of a point
• displacement ?x xf - xi change of position (
  or -)
• distance magnitude of displacement
• total distance sum of all the magnitudes of the
  displacements(equal to or larger than the
  displacement)
• velocity rate of change of position ( or -)
• average ?x/?t xf - xi/tf - ti
• instantaneous slope of x vs. t
• speed magnitude of velocity, total
  distance/time(equal to or larger than the average
  velocity)
• acceleration rate of change of velocity ( or
  -)
• average ?v/?t vf - vi/tf - ti
• instantaneous slope of v vs. t

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Skydiver Jumps Out

• A skydiver is falling straight down, along the
  negative y direction. During the initial part of
  the fall, her speed increases from 16 to 28 m/s
  in 1.5 s. Which of the following is correct?
• 1) vgt0, agt0
• 2) vgt0, alt0
• 3) vlt0, agt0
• 4) vlt0, alt0

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Parachute Opens
During a later part of the fall, after the
parachute has opened, her speed decreases from 48
to 26 m/s in 11 s. Which of the following is
correct? 1) vgt0, agt0 2) vgt0, alt0 3) vlt0,
agt0 4) vlt0, alt0
If speed is increasing, v and a are in same
direction. If speed is decreasing, v and a are in
opposite direction.
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Lecture 3, Pre-Flight Q.5
Which of the following statements is most nearly
correct? 1 - A car travels around a circular
track with constant velocity. 2 - A car travels
around a circular track with constant speed. 3-
Both statements are equally correct.

• The direction of the velocity changes when going
  around circle.
• Speed is the magnitude of velocity -- it does not
  have a direction and therefore does not change

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1D Kinematics Equations for Constant Acceleration
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1 More equation for Constant Acceleration
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Equations for Constant Acceleration

• ?x v0t 1/2 at2 (parabolic)
• ?v at (linear)
• v2 v02 2a ?x (independent of time)

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Use of Kinematic Equations - I

• Gives displacement as a function of velocity and
  time
• Use if dont know or need the acceleration

• Shows velocity as a function of acceleration and
  time
• Use if dont know or need the displacement
• Graphical interpretation ?

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Use of Kinematic Equations - II

• Gives displacement given time, velocity
  acceleration
• Use when you dont know or need the final velocity

• Gives velocity as a function of acceleration and
  displacement
• Use when you dont know or need the time

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Lecture 3, Pre-Flight Q.4

• An object is dropped from rest. If it falls a
  distance D in time t then how far will if fall in
  a time 2t ?
• 1. D/4 2. D/2 3. D 4. 2D
  5. 4D

Follow-up question If the object has speed v at
time t then what is the speed at time 2t ? 1.
v/4 2. v/2 3. v 4. 2v
5. 4v
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Free Fall Principles

• Objects moving under the influence of gravity
  only are in free fall
• Objects falling near earths surface fall with
  constant acceleration due to gravity, and
  indicated by g
• g 9.8 m/s2
• g is always directed downward
• toward the center of the earth
• Ignoring air resistance and assuming g doesnt
  vary with altitude over short vertical distances,
  free fall is constantly accelerated motion

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Free-Fall

• constant downward acceleration
• g acceleration due to gravity
• same for all bodies g9.8 m/s2
• ay -g -9.8 m/s2

Summary of Free-Fall Equations y y0 v0yt
- 1/2 gt2 vy v0y - gt vy2 v0y2 - 2g?y
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Lecture 2, Pre-Flight 2 Q. 7

• A ball is thrown straight up in the air and
  returns to its initial position. For the time
  the ball is in the air, which of the following
  statements is true?
• 1 - Both average acceleration and average
  velocity are zero.
• 2 - Average acceleration is zero but average
  velocity is not zero.
• 3 - Average velocity is zero but average
  acceleration is not zero.
• 4 - Neither average acceleration nor average
  velocity are zero.

Free fall acceleration is constant (-g) Initial
position final position ?x0 ? averaged vel
?x/ ?t 0
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Throwing Down Question
A ball is thrown downward (not dropped) from the
top of a tower. After being released, its
downward acceleration will be 1. greater than
g 2. exactly g 3. smaller than g
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Lecture 3, Pre-Flight Q. 1 2

• A ball is thrown vertically upward. At the very
  top of its trajectory, which of the following
  statements is true
• 1. velocity is zero and acceleration is zero2.
  velocity is not zero and acceleration is zero3.
  velocity is zero and acceleration is not zero4.
  velocity is not zero and acceleration is not zero

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Free Fall dropping throwing

• Drop
• Initial velocity is zero
• Acceleration is always g -9.80 m/s2
• Throw Down
• Initial velocity is negative
• Acceleration is always g -9.80 m/s2
• Throw Upward
• Initial velocity is positive
• Instantaneous velocity at maximum height is 0
• Acceleration is always g -9.80 m/s2

vo 0 (drop) volt 0 (throw) a g
v 0 a g
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Summary Constant Acceleration

• Constant Acceleration
• x x0 v0xt 1/2 at2
• vx v0x at
• vx2 v0x2 2a(x - x0)
• Free Fall (a -g)
• y y0 v0yt - 1/2 gt2
• vy v0y - gt
• vy2 v0y2 - 2g(y - y0)

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Lecture 3, Pre-Flight Q.3

• Dennis and Carmen are standing on the edge of a
  cliff. Dennis throws a basketball vertically
  upward, and at the same time Carmen throws a
  basketball vertically downward with the same
  initial speed. You are standing below the cliff
  observing this strange behavior. Whose ball is
  moving fastest when it hits the ground?
• 1. Dennis' ball 2. Carmen's ball 3.
  Same

On the dotted line ?y0 gt v2 v02 v
v0 When Denniss ball returns to dotted
line its v -v0 Same as Carmens
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Lecture 3, Pre-Flight Q.3 Follow-up

• Dennis and Carmen are standing on the edge of a
  cliff. Dennis throws a basketball vertically
  upward, and at the same time Carmen throws a
  basketball vertically downward with the same
  initial speed. You are standing below the cliff
  observing this strange behavior. Whose ball hits
  the ground at the base of the cliff first?
• 1. Dennis' ball 2. Carmen's ball 3.
  Same

Time for Denniss ball to return to the dotted
line v v0 - g t v -v0 t 2 v0 / g This
is the extra time taken by Denniss ball
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Free Fall Scenarios

• The motion may be symmetrical
• Then tup tdown
• Then v -vo
• The motion may not be symmetrical ?
• Break the motion into various parts
• Generally up and down
• Need to divide the motion into segments
• Possibilities include
• Upward and downward portions
• symmetrical portion back to releasepoint and
  non-symmetrical portion