# 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

   How should I move to reproduce the graph on
the previous slide?
Interactive Position Time Graph
1. Stand still
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

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

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 views: 99 posted: 11/15/2008 language: English pages: 30