a = Velocityfinal – Velocityinitial
time
 Solve for Velocityfinal with algebra
 A new (but old) formula
Velocityfinal= Velocityinitial + at
Velocityfinal= Velocityinitial + at
 Calculate the instantaneous speed at the 10 s mark
for a car that accelerates at 2 m/s² from a position at
rest
 Velocityfinal= Velocityinitial + at
=
0 m/s
= 20 m/s
+2 m/s² (10 s)
Free Fall
 Definition- when
an object is
moving solely
(only) under the
influence of
gravity….
Example of gravity
 Dropping a ball?
 Yes
 Yes, once it leaves
 Throwing a ball?
your hand
Experience tells you that objects speed
up (or accelerate) as they fall
 All objects
always
accelerate at
the same rate
 (when we ignore
air resistance)
Ignoring air resistance
On the moon
 http://www.youtube.com/watch?v=U7db6ZeLR5s
So what is that magical number that
all objects accelerate at?
9.8 m/s²
Finish the definition of free fall
 Definition- when an
object is moving
solely (only) under
the influence of
gravity….
 (when we ignore air
resistance)
The History of the Law of
Falling Bodies
Galileo Galilei
(1564-1642)
Galileo is said to have dropped two unequal weights from the top of the
Leaning Tower of Pisa to prove his theory.
Galileo claimed that a naturally falling object would gain equal amounts of
velocity in equal amounts of time.
If correct, this means that
i) the object’s speed increases as it
falls and
ii) the rate at which it picks up speed
does not change during the fall.
However, for medieval science, freely falling objects moved too quickly and
the clocks could not record quickly enough .
So Galileo devised to slow down the motion by replacing the
falling object with a ball rolling down a gently inclined plane.
The velocity of a free-falling object which has
been dropped from a position of rest is
dependent upon the time for which it has fallen.
Time (s)
0
1
2
Velocity (m/s)
0
9.8
19.6
3
29.4
4
39.2
5
49.0
Gravity
1) Causes free
falling objects to
accelerate at 9.8
m/s² toward the
center of the
earth.
2) The symbol is g
(for acceleration
due to gravity)
Gravity
 Positive or
negative?...that’s the
question!
 By convention….
 + 9.8 when an object is
falling towards the earth
- 9.8 when an object is
moving away from the
earth
How fast something is moving is very
different from how far
 How far does an object
fall in 1 s?
 It is 4.9 m….why?
 In free fall, the object
started from rest and is
not at a constant speed
Velocityavg=Vfinal + Vinitial
2
How far will an object drop?
 d= ½ gt²
 I drop a rock off of a
bridge, and 4.2 s later,
I hear a splash. What is
the height of the
bridge?
 d= ½ (9.8 m/s²) (4.2 s)²
= 86 m
Kinematics Formula Summary
1.
vf = vi + gt
2.
d = vi t + ½gt 2
3.
vf2 = vi2 + 2 gd
½
if velocity is 0 then the equation
Practice Problem
You drop a ball from rest off a 120 m high cliff.
Assuming air resistance is negligible (free fall), how
long is the ball in the air?
What is the ball’s speed when it strikes the ground at
the base of the cliff?
Answer
 t = 4.95s
 vf =48.5m/s
Review
 http://onlinephys.com/f
reefall6.gif
 http://onlinephys.com/f
reefall5.gif
What’s the story?
Free Fall with Upward Motion
• When something is
thrown straight upward
under the influence of
gravity, and then
returns to the thrower,
this is very symmetrical
= parabola
• The object spends half
its time traveling up;
half traveling down.
Free Fall with Upward Motion
• Velocity when it
returns to the ground is
the opposite of the
velocity it was thrown
upward with.
• Acceleration is 9.8 m/s2
and directed DOWN
the entire time the
object is in the air!
Free Fall with Upward Motion
Free Fall with Upward Motion
 Homer Hickham used
this fact to determine
how high his rocket
went and that the
rocket boys didn’t start
the fire in Welch
October Sky
 http://www.youtube.com/watch?v=udHB3tftPz4