Physics 218

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Physics 218
Lecture 4 Kinematics

• Alexei Safonov

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  (elearning.tamu.edu) except HW
• HW will be on Mastering Physics, HW score will be
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  at the end of the semester

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Todays Lecture

• Finish up some math issues
• Integrals
• Problem solving techniques
• Motion in 1-Dimension continued
• No longer going to use numbers
• Examples
• Stopping a speeding car
• Free fall
• Catching a speeder

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Important Equations of Motion

• If the acceleration is constant
• Position, velocity and Acceleration are vectors.
  More on this in Chap 3

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Problem with Derivatives

• A car is stopped at a traffic light. It then
  travels along a straight road so that its
  distance from the light is given by
• x(t) bt2 - ct3, b 2.40 m/s2, c 0.12 m/s3
• Calculate
• instantaneous velocity of the car at t 0,5,10 s
• How long after starting from rest is the car
  again at rest?

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Getting Displacement from Velocity
For const acceleration the Equation of motion
XX0V0t ½at2

• If you are given the velocity vs. time graph you
  can find the total distance traveled from the
  area under the curve
• X-X0V0t ½at2
• Can also find this from integrating

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A car is moving with velocity given by a known
formula v(t)abtct3.Is this information
sufficient to calculate the position of the car
at some tT?

• Yes, position can always be calculated using x(t)
  ?v(t) dt
• No, because one also has to know acceleration
  a(t)
• No, because one also has to know initial position
  of the object, e.g. at t0
• No, because acceleration is not constant

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Definite and Indefinite Integrals
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Some Integrals
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Our Example with Const. Acceleration
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How quickly can you stop a car?

• Youre driving along a road at some constant
  speed, V0, and slam on the breaks and slow down
  with constant deceleration a.
• How much time does it take to stop?
• How far do you travel before you come to a stop?

Where you stop
When you hit the brakes
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Free Fall

• Free fall is a good example for one dimensional
  problems
• Gravity
• Things accelerate towards earth with a constant
  acceleration
• ag9.8m/s2 towards the earth
• Well come back to Gravity a lot!

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Throw a Ball up

• You throw a ball upward into the air with initial
  velocity V0. Calculate
• The time it takes to reach its highest point (the
  top).
• Distance from your hand to the top
• Time to go from your hand and come back to your
  hand
• Velocity when it reaches your hand
• Time from leaving your hand to reach some random
  height h.

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Problem

• Show that for constant acceleration

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Speeder

• A speeder passes you (a police officer) sitting
  by the side of the road and maintains their
  constant velocity V. You immediately start to
  move after the speeder from rest with constant
  acceleration a.
• How much time does it take to ram the speeder?
• How far do you have to travel to catch the
  speeder?
• What is your final speed?

X
Police Officer Speeder
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Graphs

• Describe motion in each point
• Direction
• Velocity
• Acceleration

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Next Week

• Reading and Lecture Chapter 3, Motion in two or
  three dimensions
• Reading Quiz (clickers, at the end of the class)
  
• Pay attention to Discussion Questions Q3.1-3.6
  Q3.17-3.18,
• Recitation and Homework
• HW Chapter 1 HW is due Monday noon
• Next Recitation Chapter 2 and Quiz
• One of the problems from Ch.2 HW

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YF 2.95 (Challenge Problems)

• Catching the bus a student is running at 5m/s to
  catch a bus. When it is 40 m to the bus, the bus
  starts moving with constant acceleration a0.170
  m/s2.
• Questions
• For how much time and what distance does the
  student have to run to overtake the bus?
• When she reaches the bus, what is the bus
  velocity
• Sketch an x-t graph for both the student and the
  bus
• First question has two solutions. What do those
  mean and what is the speed of the bus at that
  moment?
• What is the minimum speed the student must have
  to catch up with the bus?

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Car Crash Test Design

• You are designing a crash test setup for a car
  maker. You can accelerate a car from rest with a
  constant acceleration of 1.00 m/s2 so you can
  make the car crash into a wall. (This is the last
  time you will see numbers in a problem in
  lecture).
• If the path is 200m long, what is the velocity of
  the car just before/as it hits the wall?
• For the same acceleration, if you want the car to
  hit the wall with a speed of 30m/s (about 60
  mi/hr), what minimum length must you have?

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YF Problem 2.9

• A car is stopped at a traffic light. It then
  travels along a straight road so that its
  distance from the light is given by
• x(t) bt2 - ct3, b 2.40 m/s2, b 0.12 m/s3ct
• Calculate
• instantaneous velocity of the car at t 0,5,10 s
• How long after starting from rest is the car
  again at rest?