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.
   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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