Uniform Motion by Vz1jTCk1

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									   Chapter 2

Uniformly Accelerated
       Motion
      Speed
                total distance traveled
Average Speed 
                       time taken

                  s
            vav 
                  t
       Velocity
                   vector displaceme nt
Average Velocity 
                        time taken
                  
                 s
            vav 
                  t
          Acceleration
                        change in the velocity vector
Average Accelerati on 
                                 time taken
                       
                     v f  vi   v
       aav                    
                       t f  ti t
            What are the units for acceleration?
Uniformly Accelerated Motion
Along a Straight Line
    In this case…
        • acceleration is a constant
        • and the acceleration vector lies in the
          line of the displacement vector.
The 5 Equations!
          (1)   s  si  vi t  at 1
                                   2
                                       2



          (2)   v f  vi  at

          (3)   v  v  2as
                   2
                   f
                        2
                        i


          (4)   s  vavt
                        v f  vi
          (5)   vav 
                            2
          Problem Solution Guidelines

   Draw a sketch
    – Indicate origin and positive direction
   List the given quantities using the symbols of the
    equations. (si, vi, a)
    – Is time known or do we need to find it?
    – What are we to solve for?


   Write the general equations of kinematics
           v f  vi  at         s  si  vi t  1 at 2
                                                 2
         More Guidelines

   Rewrite the general equations using the
    known quantities.
   Look at the knowns and unknowns and map
    a strategy of solution.
   Check your units
   Make sure you are answering the question.
         Problem Solution Time

   Fifteen minutes
         Definitions

   Instantaneous Velocity
    – the slope of the displacement versus time graph


   Instantaneous Acceleration
    – the slope of the velocity versus time graph
               Slopes
Displacement




                          A

                  B


                   Time
Teaming Exercise
  Next Problem solutions
      Free Fall

   The force of gravity points downward
    – Acceleration of gravity near the surface of
      Earth is called g = 9.8 m/s2 = 32.1 ft/s2
   Air resistance ignored

   We have then the conditions of one-
    dimensional kinematics – straight line
    motion with constant acceleration.
         Sample Problem

   A ball is thrown vertically upward at 10
    m/s. How high will it get, how long will it
    be in the air, and how fast will it be moving
    when it hits the ground.
Projectile Problems – Two
Dimensional Kinematics

   Ignore air resistance.

   ax = 0

   ay = g = 9.81 m/s2 downward
             The motions in the two
             directions are independent
Horizontal

Vertical
Real Motion is the
Combination of the Two
2-D Problem Guidelines

   Set up two 1-D solutions

Origin x          Origin y
Positive x        Positive y
xi =              yi =
vxi =             vyi =
ax = 0            ay = g
         2-D Guidelines Cont’d

   Write general kinematic equations for each
    direction
   Rewrite them for the problem at hand
   Find the condition that couples the motions
    (usually time)
         Uniformly Accelerated
         Motion Along a Straight Line

  s  vavt
                      s  vi t  at
                                1
                                2
                                      2

        v f  vi
vav                 v f  vi  at
           2

                     v  v  2as
                      2
                      f
                            2
                            i

								
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