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Kinematics In One Dimension (PowerPoint)

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									Kinematics In One Dimension
        What Is Kinematics?
• Kinematics are the concepts that describe

• We don’t care why an object moves. We
  only care that it moves.

• We will be using 5 different quantities to
  describe the motion of an object.
    Five Quantities Describing Motion
•   Displacement (d) – measured in meters
•   Initial Velocity (vo) – measured in m/s
•   Final Velocity (vf) – measured in m/s
•   Acceleration (a) – measured in m/s2
•   Time (t) – measured in seconds
       Positive and Negative
• You must assign a positive and a negative
  direction to all problems.

• The positive and negative directions give
  your values a positive or negative sign and
  vice versa
• Displacement (x) is a vector that points
  from an object’s initial position to its final
  position and has a magnitude that equals
  the shortest distance between the two
• Velocity is a vector quantity that is given
  by an object’s change in displacement
  divided by the time interval during which
  the change took place.
            Constant Velocity
• When an object is moving at a constant
  velocity (NO speed changes or direction
  changes) its velocity can be found by:

• v = d/t

• d = displacement
• t = time
     How Far Does He Run?
• How far does a jogger run in 1.5 hours if
  his average speed is 2.22 m/s?

• 11988 m
            They’re Good
• Ryan Hall runs a 10.0 km course with an
  average speed of 4.39 m/s. Deena Kastor
  covers the same distance with an average
  speed of 4.27 m/s. How much later (in
  seconds) should Ryan Hall leave to finish
  at the exact same time as Deena Kastor?
             Sunday Drive
• You drive a car 2.0 hours at 40 km/h, then
  2.0 h at 60 km/h.

• What is your average velocity?
• Do you get the same answer if you drive
  100 km at each of the two speeds above?
             Stop That Car
• You’re driving down a street at 55 km/h.
  Suddenly a child runs into the street. If it
  takes you 0.75 s to react and apply the
  brakes, how many meters will you have
  traveled before you begin to slow down?
           Relative Velocity
• Velocity is based off of a reference point.

• Consider when you drive down the road in
  your car.

• What’s your velocity compared to a traffic
• What’s your velocity compared to your
  drink in the cup holder?
            Buggies Collide
• Today you will be colliding two constant
  velocity buggies.
• You will need to find the velocity of both of
  the buggies you intend to use.
• You will set each buggy at opposite ends
  of a track.
• You will have to predict where the buggies
  will collide.
• You are being grades on your accuracy
  only! Be sure you’re correct before you
  attempt your collision.
               Car Crash
• A driver falls asleep behind the wheel of a
  car and drifts into the oncoming lane. The
  sleeping driver is going 16 m/s and an
  oncoming car is going 20 m/s. If they are
  85 m apart when will they collide and
  where will they collide using the sleeping
  driver’s start as your reference point.
• Acceleration is a vector quantity. It is
  defined as the change in an object’s
  velocity over the time interval during which
  the change takes place.
      Constant Acceleration
• There are 4 equations that we can use to
  fully describe the motion of an object.

• These equations only work for Constant
          Ready For Liftoff
• Determine the displacement of a plane
  that uniformly accelerated from 53 m/s to
  75 m/s in 12 seconds.
    This Is Why You Shouldn’t
• A race car can be slowed with a constant
  acceleration of –8 m/s2. How many meters
  will it take the car to stop if it is initially
  traveling at 55 m/s?

• What if it was initially moving at 110 m/s?
                Take Off
• An airplane must reach a velocity of 71
  m/s for takeoff. If the runway is 1.0 km
  long, what must the constant acceleration
            Target Practice
• If a bullet leaves the muzzle of a rifle with
  a speed of 600 m/s, and the barrel of the
  rifle is 0.9 m long, what is the acceleration
  of the bullet while it is in the rifle?
• In which one of the following
  situations does the car have a
  westward acceleration?
• (a) The car travels westward at constant
• (b) The car travels eastward and speeds up.
• (c) The car travels westward and slows down.
• (d) The car travels eastward and slows down.
• (e) The car starts from rest and moves
  toward the east.
               Darn Truck
• As a traffic light turns green, a waiting car
  starts with a constant acceleration of 5.0
  m/s2. At the instant the car begins to
  accelerate a truck with a constant velocity
  of 24 m/s passes in the next lane.
• How far will the car travel before it
  overtakes (is side by side again with) the
• How fast will the car be traveling when it
  overtakes the truck?
Where Did Those Equations Come
• The four kinematics equations of constant

• How did we get them?

• What exactly do they mean?
You Have To Consider The Graphs
• Consider the 1st equation:
• vf = vo + at

• Now consider a velocity vs. time graph for
  an object undergoing constant
V vs. T
            d = ½ (vo + vf)t
• This also comes from a v vs. t graph
  (Only under constant acceleration)
      What About The Others?
• The other two equations come from
  combining the previous two equations.
• vf = vo + at & d = ½ (vo + vf) t

• d = vo + ½ at2

• v f2 = v o2 + 2ad
• Why have graphs? What do they tell us?

• We can learn about the motion by looking
  at both slope and area under the curve of
  different graphs.

• d vs. t, v vs. t, a vs. t
       Displacement vs. Time
• What does a displacement vs. time graph
  tell us?

• The slope of a line on an x vs. t graph tells
  you about velocity.

• The area under the curve tells you
          Velocity vs. Time
• What does a velocity vs. time graph tell

• The slope tells us about the acceleration.

• The area under the curve tells us about
       Acceleration vs. Time
• What does an acceleration vs. time graph
  tell us?

• The slope tells us nothing.

• The area under the curve tells us velocity.
    Questions To Ask Yourself
• Is the slope a constant? (a straight line
  with any slope)

• Is the slope not a constant? (a curved line
  of any kind)
       Two Types Of Motion
• We will deal with only two types of motion
  in this class. (That does not mean that
  these are the only two types of motion)

• Non-accelerated motion

• Constant acceleration motion

• Here are what their graphs look like.
Non-Accelerated Motion
Constant Acceleration Motion
        Buggies & Fan Cars
• We are now going to repeat our Buggies
  Collide lab only now we are going to be
  using a Buggy and a Fan Car.

• Don’t forget the Fan Car is accelerating.
   Acceleration Due To Gravity
• Acceleration due to gravity (g) is the
  acceleration that all objects falling toward
  the Earth possess.

• On the surface of the Earth g = 9.8 m/s2
  toward the Earth.

• Whenever an object is in freefall
  a = g = 9.8m/s2 down
             Drop A Rock
• A student drops a rock from a bridge to the
  water 12.0 m below. With what speed
  does the rock strike the water?
• A particle travels along a curved path
  between two points P and Q as shown.
  The displacement of the particle does not
  depend on

•   (a) The location of P
•   (b) The location of Q
•   (c) The distance traveled from P to Q
•   (d) The shortest distance between P & Q
•   (e) The direction of Q from P
• The greatest height reported for a jump
  into an airbag is 99.4 m by stuntman Dan
  Koko. In 1948 he jumped from rest from
  the top of the Vegas World Hotel and
  Casino. He struck the airbag with a speed
  of 39 m/s (88 mi/h). To assess the effects
  of air resistance determine how fast he
  would have been traveling on impact had
  air resistance been absent.
• Ball A is dropped from rest from a window. At the
  same instant, ball B is thrown downward; and ball C is
  thrown upward from the same window. Which
  statement concerning the balls after their release is
  necessarily true if air resistance is neglected?
• (a) At some instant after it is thrown, the acceleration
      of ball C is zero.
• (b) All three balls strike the ground at the same time.
• (c) All three balls have the same velocity at any
• (d) All three balls have the same acceleration at any
• (e) All three balls reach the ground with the same
               Heads Up
• Assuming that the arrow lands 2 m below
  where it was shot find the max height of
  the arrow and how fast it was moving
  when it landed.
• Two objects A and B accelerate from rest with the
  same constant acceleration. Object A accelerates for
  twice as much time as object B, however. Which one
  of the following statements is true concerning these
  objects at the end of their respective periods of

• (a) Object A will travel twice as far as object B.
• (b) Object A will travel four times as far as object B.
• (c) Object A will travel eight times further than object B.
• (d) Object A will be moving four times faster than
  object B.
• (e) Object A will be moving eight times faster than
  object B.
             Get Wrecked
• A wrecking ball is hanging from a crane
  when suddenly the cable breaks. The time
  it takes for the ball to fall halfway to the
  ground is 1.2 seconds. Find the time it
  takes for the ball to fall from rest all the
  way to the ground.
• In the process of delivering mail, a postal
  worker walks 161 m, due east from his
  truck. He then turns around and walks
  194 m, due west. What is the worker’s
  displacement relative to his truck?

•   (a) 33 m, due west
•   (b) 194 m, due west
•   (c) 355 m, due west
•   (d) 33 m, due east
•   (e) 252 m, due east
        How Does It Move?
• Describe the velocity and acceleration
  over each colored section.
• An object moving along a straight line is
  decelerating. Which one of the following
  statements concerning the object’s acceleration
  is necessarily true?
• (a) The value of the acceleration is positive.
• (b) The direction of the acceleration is in the
  same direction as the displacement.
• (c) An object that is decelerating has a negative
• (d) The direction of the acceleration is in the
  direction opposite to that of the velocity.
• (e) The acceleration changes as the object
  moves along the line.
           Look Out Ahead
• While you’re in your car traveling down the
  road at 23 m/s a dog runs into the road 35
  m ahead. If you immediately hit the brakes
  and slow at a rate of 8 m/s will you be able
  to stop in time to avoid hitting the dog?
  How far short or beyond the dog do you
• Starting from rest, a particle confined to move
  along a straight line is accelerated at a rate of
  5.0 m/s2. Which one of the following statements
  accurately describes the motion of this particle?
• (a) The particle travels 5.0 m during each
• (b) The particle travels 5.0 m only during the first
• (c) The speed of the particle increases by 5.0
  m/s during each second.
• (d) The acceleration of the particle increases by
  5.0 m/s2 during each second.
• (e) The final speed of the particle will be
  proportional to the distance that the particle

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