How To Go Nowhere Fast

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					How To Go Nowhere
      Fast…
Displacement, Velocity and
       Acceleration
    More Trig…
   Pythagorean Theorem

         r 2  x2  y 2

   To find an angle, you need
    the inverse trig function
      i.e.


       x=y=1

       What is r? ?
Dynamics & Kinematics
   Dynamics is the study of motion and of
    physical concepts
                   (i.e. relationship between force and mass)


   Kinematics is a part of dynamics
       description of motion
       Not concerned with the cause of the motion
Quantities in Motion
   Any motion involves three concepts
     Displacement
     Velocity
     Acceleration


   These concepts can be used to study objects
    in motion
Section 1.1:
Displacement
   Defined as the change          Displacement vs. Time graph
    in position
        d  d f  d i                         d

           f stands for final
           i stands for initial


                                     di                  df
   SI units are meters (m)
Displacement vs. Distance
Displacement is NOT the same as Distance

i.e. Throw a ball straight up and then catch it at
    the same point you released it

   The distance is twice the height
   The displacement is zero
Vector & Scalar Quantities
Vector
 has magnitude & direction
i.e.    
        v    - instantaneous velocity
        
        a    - instantaneous acceleration


Scalar
 has magnitude only (v, t, mass)
Section 1.2:
Speed
Speed
    the total distance traveled divided by the
    total time elapsed
                      d total
                vav 
                      ttotal

   Speed is a scalar quantity

   Average speed completely ignores any
    variations in the object’s actual motion
Average Velocity…
   Velocity is the rate of change of displacement
    per unit time

              d d f  d i
        vav     
              t   t f  ti
                                        Slope is velocity!!!


   Units?
                 [v ]  m
                            s
Speed vs. Velocity




Cars on both paths have the same average velocity… Why?
 … they have the same displacement (in the same time interval).


The car on the blue path will have a greater average speed…Why?
 … the distance it travels is larger (in the same time interval)!
   Graphical Interpretation of Velocity
       Average velocity equals the slope of the line
        joining the initial and final positions (vs. time)
             x xB  x A
       vav    
             t t B  t A
A – start at 30m from start and decelerate (neg.
   acceleration) to B

B – Velocity is 0 m/s Start to accelerate in
   reverse

C – Constant velocity in reverse.

D – At start position. Continue in reverse at
constant velocity

E – Begin to accelerate in forward direction
(slow down in reverse). Stop at F.
Position vs. Time Graphs
What will the position vs. time graph look like for
  the following:
        1. Stand still
        2. Slow steady walk
        3. Fast steady walk



   How should I move to reproduce the graph on
    the previous slide?
Interactive Position Time Graph
 1. Stand still
 2. Slow steady walk
 3. Fast steady walk
1-D Vector Problem
Two boats start together and race across a 60-km-wide
    lake and back. Boat A goes across at 60 km/h. Boat
    B goes across at 30 km/h, and its crew, realizing
    how far behind it is getting, returns at 90 km/h.
    Turnaround times are negligible, and the boat that
    completes the round trip wins.

a.   Which boat wins and by how much? (Or is it a tie)?
b.   What is the average velocity of the winning boat?
Section 2.4:
Acceleration
   the rate of change in velocity per unit time
                       (v/ t)


                   v v f  vi
                a   
                   t t f  ti

   Units?       [a ]  m
                            s2
Graphical Interpretation of
Average Acceleration
   Average acceleration equals the slope of the
    line joining the initial and final velocities (vs.
    time)

       v v f  vi
    a   
       t t f  ti
Quick Quiz…
   Match each velocity vs. time graph to its
    corresponding acceleration vs. time graph.
Section 2.4: Motion Diagrams
(Relationship between a and v)




   Uniform velocity

What is the acceleration?
    a=0
Relationship Between a and v




   v and a are in the same direction

   a is constant

   v is increasing
Relationship Between a and v




     v and a are in opposite directions

     a is constant

     v is decreasing
1. Which car or cars (red, green, and/or blue) are
undergoing an acceleration? Study each car individually in
order to determine the answer.




   Red car – moves at a constant velocity
   Green Car – accelerates
   Blue Car - accelerates
2. Which car (red, green, or blue) experiences the
greatest acceleration?




  Blue Car – Has the greatest acceleration
  Green Car – Has the 2nd greatest acceleration
  Red car – does not accelerate
3. Match the appropriate line to the
particular color of car.




  Blue Car      Green Car       Red car
Acceleration in Motion
 Animated Car Graphs
d vs. t v vs. t a vs. t
Positive Velocity, Positive
Acceleration
 If you have positive velocity and positive
 acceleration you are going forward increasing your
 velocity.
Positive Velocity, Negative
Acceleration
 If you have positive velocity and negative
 acceleration you are going forward but slowing down
Negative Velocity, Positive
Acceleration
 If you have negative velocity and positive
 acceleration you are going backwards and slowing
 down in that direction.
 At some point you would start moving forward ....
Negative Velocity, Negative
Acceleration
 If you have negative velocity and negative
 acceleration you are going backwards and speeding up
 in that direction.
Positive and Negative Velocity and
Acceleration
 Velocity   Acceleration          Action
 Positive     Positive     Car is speed up in the
                            forward direction

 Positive     Negative     Car is slowing down in
                           the forward direction

 Negative     Positive     Car is slowing down in
                            the reverse direction

 Negative     Negative     Car is speeding up in
                           the reverse direction