Free Falling Objects:
Acceleration Due to
Gravity
Kinematics Unit
 Galileo
discovered that objects fall to earth
with a uniform, (constant), acceleration.
 This
constant acceleration is called the
acceleration due to gravity. This constant
is written as g = 9.81 m/s2 or
a = 9.81 m/s2.
 YOU
DO NOT USE ANY NEW
ACCLERATION FORMULAE to solve
these problems.
 For all the problems a = 9.81 m/s2.
 All
of the previously mentioned formulae
can be used because the object in
question is accelerating uniformly.
RECALL:
d
(v f  vi )
2
t
v v f  vi
a

t
t
v f  vi  2ad
2
2
1 2
d  vi t  at
2
1 2
d  v f t  at
2
 Since
acceleration is a vector, then the
acceleration due to gravity must also be a
vector, (have magnitude and direction).
 If the object is dropped or falling
a = + 9.81 m/s2 .
 If
the object is thrown upwards
a = - 9.81 m/s2.
Example 1: An object falls to the ground in
3.0s .
a. What is the object’s final velocity?
a  9.81m / s
2
vi  0
t  3.05s
+
vf  ?
v v f  vi
a

t
t
vf  0
2
9.81m / s 
3.0 s
v f  (9.81m / s 2 )(3.0 s )
v f  29m / s [ down]
b. How far does the object fall?
a  9.81m / s
vi  0
t  3.05s
d ?
2
1 2
d  vi t  at
2
1
d  (9.81m / s 2 )(3.0s) 2
2
d  44m, [down]
 Example
2: A stone is dropped from a cliff
400m high. What is displacement of the
stone after falling for 5.0 s?
1 2
d  vi t  at
2
1
d  0  (9.81m / s 2 )(5.0 s) 2
2
d  122.625
d  123m
 Example
3: A ball is thrown vertically
downwards at 30.0m/s. Determine the
instantaneous velocity of the ball at 4.00 s.
v f  vi
vi  30.0m / s
a
a  9.81m / s
t  4.00s
9.81m / s 
vf  ?
2
t
2
v f  30.0m / s
4.00 s
39.24m / s  v f  30.0m / s
69.24m / s  v f
v f   69.24m / s
Example 4: A stone is dropped from rest into
a gorge. Determine the distance that the
stone falls during the third second of the fall.
vi  0m / s
a  9.81m / s 2
t  3.0 s
d ?
1 2
d  vi t  at
2
1
2
2
d  0  (9.81m / s )(3.0 s )
2
d  44.1m (sig digs are undetermined because
the question was all words and no numbers)
Assignment:
Read Text p. 54 – 62 Do p. 58 # 1-3 p.60 #1
 Do Workbook p. 45 #25 – 33 (omit the question
that requires you to use the CD that came with
the book)

NOTE:
 No class: Monday Sept. 28 (River Watch)
 Quiz on Accelerated Motion and Graphing:
Wednesday, Sept. 30
 Accelerated Motion Lab due Wednesday, Sept.
30