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

aav 
 
v f  vi
v

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
(2)
v f  vi  at
(3)
v  v  2as
(4)
s  vavt
(5)
1
2
2
f
vav 
2
i
v f  vi
2
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  12 at 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
Displacement
Slopes
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 onedimensional 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
Positive x
xi =
vxi =
ax = 0
Origin y
Positive y
yi =
vyi =
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
vav 
v f  vi
2
s  vi t  at
1
2
v f  vi  at
v  v  2as
2
f
2
i
2