Physics 103: Lecture 4 Position

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Physics 103 Lecture 4Position Velocity with
constant Acceleration

• Todays lecture will be on kinematic equations
• 1D motion with constant acceleration
• free-fall
• Introduction to 2D motion

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Summary of Concepts (from last lectures)

• 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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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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1D Kinematics Equations for Constant Acceleration
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2 More equation for Constant Acceleration
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Use of Kinematic Equations - I

• Gives position given time, velocity
  acceleration
• Displacement can be found by calculating x-x0
• Use when you dont know or need the final velocity

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

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Use of Kinematic Equations - II

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

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

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Question?
I am going to roll the ball down the inclined
plane. If the ball reaches mark at distance 1 ft
at time t1, when will the ball reach the mark at
distance 9 ft? 1. t9 9t1 2. t9 v18
t1 3. t9 3t1
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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
• Most common example of constant acceleration

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

vo 0 (drop) volt 0 (throw) a g
v 0 a g
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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
v v0- g t t 2 v0 / g v -v0
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Free Fall Scenarios

• Is the motion symmetrical?
• Then tup tdown
• Then v -vo
• The motion may not be symmetrical ?
• Break the motion into various segments
• Are there symmetrical segments?
• Possibilities include
• Upward and downward portions
• symmetrical portion back to releasepoint and
  non-symmetrical portion

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A battleship simultaneously fires two shells at
enemy ships from identical canons. If the shells
follow the parabolic trajectories shown, which
ship gets hit first? 1. Ship A. 2. Ship
B. 3. Both at the same time
Higher the shell flies, the longer it takes.
What should the captain order if he wants to hit
both ships at the same time?
A
B