CH. 3 ACCELERATION
Rate of change of velocity
CONSTANT & CHANGING VELOCITY
• Velocity is CONSTANT as long as its speed and direction
are constant
• If either is changing then velocity is not constant
• Velocity constant if…
 Object is at rest (not moving)…….or
 Object is moving in a straight line at a constant
speed
ACCELERATION
 Occurs when an object….
 Speeds up
 Slows down
 Changes direction
 The rate at which velocity changes with
time
DESCRIBE THE VELOCITY & ACCELERATION
IN THE FOLLOWING DIAGRAMS
(ASSUME EACH PICTURE REPRESENTS 1 SEC OF TIME)
At Rest
Speeding up (positive
acceleration)
Constant Velocity
Slowing down (negative
acceleration)
DETECTING VELOCITY & ACCELERATION
 Human body cannot detect velocity
 Accelerations easy to detect
 Examples
AVERAGE ACCELERATION
 Change in Velocity / change in time
v v f  vi
a

t
t
 Measures the rate of change of an object’s velocity
 If the magnitude or direction of velocity is changing, then an
acceleration must be occurring
 Average Acceleration:
2 or any unit length over a unit time over a unit
 Units-- m/s
time
 Vector quantity so + or - depending on the direction
ACCELERATION TABLE
-OBJECT STARTING FROM REST AND UNDERGOING AN ACCELERATION
OF 3 M/S2
Time (sec)
Inst.Velocity Acceleration
(m/s)
(m/s2)
Position
(m)
Displaceme
nt per
second (m)
0
0
3
0
0
1
3
3
1.5
1.5
2
6
3
6
4.5
3
9
3
13.5
7.5
4
12
3
24
10.5
ANOTHER ACCELERATION TABLE
-OBJECT WITH AN INITIAL VELOCITY OF 24 M/S, THEN UNDERGOING
AN ACCELERATION OF – 4 M/S2
Time (sec)
Inst.Velocity Acceleration
(m/s)
(m/s2)
Position
(m)
Displaceme
nt per sec
(m)
0
24
-4
0
0
1
20
-4
22
22
2
16
-4
40
18
3
12
-4
54
14
4
8
-4
64
10
5
4
-4
70
6
6
0
-4
72
2
INSTANTANEOUS ACCELERATION …
o Acceleration is often not sustained for very long
(real life), so will not remain constant
o Acceleration at a given instant in time -Instantaneous Acceleration
o ** Most situations we deal with are with
Constant (Uniform) Acceleration
o This means….. Instantaneous is equal to Avg
at all times
GRAPHS OF MOTION
 Motion can also be depicted very well using graphs
 Two types of graphs
 Position vs. time graphs (below on left) --- as
Velocity (m/s)
Position (m)
already discussed
 Velocity vs. time graphs (below on right)
SLOPE REVISITED
 Slope = rise/ run
 how much the graph goes up divided by how much the graph
goes across
 ∆y /∆x
 Slope tells us important traits of the motion being depicted
slope = avg. velocity
 slope = avg. acceleration
 On a Position-time graph 
 On a Velocity-time graph
 Velocity-time graph
 Rise =Δy =Δv
◦ 16
 Run = Δt
◦ 4
 Rise/run = Δv / Δt = a
◦ 4 m/s2 = acceleration
Velocity (m/s)
 Slope = rise/run …
Time (s)
position(m)
Time interval
Avg Vel. For interval
0
0
0-1 s
8 m/s
1
8
1-2 s
3 m/s
2
11
2-3 s
7 m/s
3-4 s
-3 m/s
3
18
4-5 s
10 m/s
4
15
1-4 s
3.33 m/s
5
25
0-5 s
5 m/s
2-4 s
2 m/s
30
25
(m)
Position
Velocity (m/s)
20
15
10
5
0
0
1
2
3
Time (S)
4
5
6
A- Constant negative velocity
B- At rest w/ a positive position
C- At rest w/ a negative position
D- Slow Constant positive
Velocity
E- Faster Constant positive
Velocity
F- Positive Acceleration
G- Negative Acceleration
COMPARING GRAPHS
 P-t graphs
E
Position (m)
A
F
G
B
Time (s)
C
D
A- Constant negative acceleration
B- Constant positive Velocity
C- constant Negative Velocity
D- Slow Constant positive Acceleration
E- Faster Constant positive Acceleration
F- At Rest
COMPARING GRAPHS
 V-t graphs
Velocity (m/s)
A
E
D
B
F
Time (s)
C
ACCELERATION & VELOCITY DIRECTION
First 10m of race, starting from rest…
 Assume start line is origin
xf > xi, so Δx is positive
 Average velocity is positive
vf > vi, so v is positive
 Acceleration is positive
ACCELERATION & VELOCITY DIRECTION
 10m after crossing finish line and
coming to a stop…
 Still assuming start line is
reference point
 xf > xi, so Δx is positive
 Average velocity is still positive
 vf < vi, so v is now negative
 Acceleration is negative
ACCELERATION AS A VECTOR QUANTITY
 Acceleration is a vector quantity
 Direction must be expressed
 Acceleration tells how velocity is changing, but it doesn’t always have
to be in the same direction as velocity
 If acc. & vel. have the same sign → speeding up
 If acc. & vel. have opposite signs → slowing down
VELOCITY & ACCELERATION
WHAT HAPPENS TO MOTION, BASED ON
VELOCITY AND ACCELERATION?
Initial Velocity
+
+
+ or -
Acceleration
+
+
0
0
+ or -
Motion
Speeding Up
Slowing Down
Slowing Down
Speeding Up
Constant V
Speeding up
from rest
VELOCITY VS. TIME GRAPH OF CONSTANT
ACCELERATION
 How to find instantaneous velocity from graph at a certain
time? …. Follow
x-value for ‘t’
corresponding y value for ‘v’ for every
 How to find average velocity from graph??

1
vavg  (v f  vi )
vavg is midpt between Vi and
2 Vf when acc. is constant
substitute ½(vf +vi) in for vavg and we get
Δx= ½(vf+vi)t
◦ This coincidentally will always equal the
the graph
Velocity (m/s)
 How to find displacement from graph?
◦ Remember vavg=Δx/t
so Δx=(vavg)t and
area under
A POSITION-TIME GRAPH OF CONSTANT
ACCELERATION…. A PARABOLA
 Line getting steeper and steeper…
 slope increasing  velocity
increasing
 Velocity is different every instant
INSTANTANEOUS SPEED VS. AVG SPEED
 Slope of the tangent line graph
=instantaneous speed at that time
 How to find average velocity over a
certain interval??
◦ Same as always… vavg=x/t
AVERAGE VELOCITY WHEN THERE IS AN
ACCELERATION…
 -Average velocity during a constant acceleration is equal to the
midpoint between the initial and final velocity
 -Vav= ½(vf +vi)
KINEMATICS EQUATIONS …
YOUR NEW BEST FRIENDS!!
 Vf=vi+at
◦
from acceleration equation
 Vav= ½(vf +vi)
 Previous slide
 Xf = xi + ½ (vf + vi)t
◦
From combining two equations for average velocity.
 xf =xi + vit + ½ at2
◦
From combining 1st and 3rd equations… derivation shown on board
 Vf2 = vi2 +2a(Δx)
◦
From substituting Vf=vi+at into 4th equation
HOW TO FIND ΔX FROM A V-T
GRAPH
• Find the area under the curve
 Area between the line and x-axis
 Break into shapes
• The process agrees with equation Xf = xi + ½ (vf + vi)t
•
3.4 FREE FALL ACCELERATION
• When objects are ONLY under the influence of
gravity
• As objects fall toward the Earth they are accelerating
at a rate of
g = 9.81 m/s2

• For FREE Fall
a = -g = - 9.8m/s2
• An object doesn’t necessarily have to be ‘falling’ to be
in free fall…
- can be moving upwards
Time
(sec)
Insta
ntane
ous
Spee
d
(m/s)
Accele
ration
(m/s2)
0
0
-9.81
1
-9.81
-9.81
2
-19.62
-9.81
3
-29.43
-9.81
4
-39.24
-9.81
• When in the absence of air resistance and around the surface of the Earth
ALL OBJECTS will fall with a downward acceleration of g=9.81 m/s2
CURVATURE OF
GRAPH TELLS
ACCELERATION