Kinematics and Free Fall
Calculations of a Symmetrical Path
Kinematical Equations
Often, it is useful to relate
position, velocity, and
constant acceleration.
The three equations for
motion with constant
acceleration are
summarized in the table.
Kinematical Equations
Acceleration Due to Gravity = 9.8m/s2
Suppose the free-fall ride at an amusement park starts at rest
and is in free fall for 1.5 s. What would be its velocity at the end
of 1.5 s?
*Because the car starts at rest,
vi would be equal to 0.00 m/s.
Kinematical Equations
How far does the car fall?
Use the equation for displacement when time
and constant acceleration are known.
Falling
Air resistance will
increase as it falls
faster
An upward force on the
object
Eventually gravity will
balance with air
resistance
Reaches terminal
velocity - highest speed
reached by a falling
object.
Terminal velocity
Force of gravity is constant
air
resistance increases
as
you speed up
 until the force is equal

Equal forces, no
acceleration

constant velocity at
terminal velocity
THROWING OBJECTS UP
Final speed up
We talked about what
happens when an object is
thrown into the air…
• It slows down as it go
up.
• At the highest point, it
stops.
• As it falls, it speeds
up… We have done the
falling objects.
=
Gravity is slowing
the object
down… -9.8 m/s2
Initial speed up
Initial speed down
Gravity is speeding the
object up… +9.8m/s2
=
Final speed down
Going up!
When throwing an object
into the air, an initial speed
must be given to the object.
If the object is a stomp
rocket, then the AIR is what
gives the rocket its initial
speed.
At the top of the flight… the
highest point… the speed is
0.
Gravity is slowing the object
down with an acceleration of
– 9.8 m/s2.
Going Down!
This is what we have
done before.
When dropping
something, initial
speed is 0.
An object falls
because of gravity
with an acceleration of
9.8 m/s2.
Symmetry
What goes up must come down… and in a
symmetrical pattern.
What is symmetry?
A regular arrangement,
corresponding in size, form, and arrangement
of parts on opposite sides of a line
• In other words, both sides are even
• The up side looks exactly like the down side, except for
direction.
Because of Symmetry…
Since the initial speed up is the same as the
final speed down…
Since the initial speed down is the same as
the final speed up…
Since gravity is 9.8 m/s2, even though one is
positive and one is negative…
Since the object travels the same distance
up as it does down…
Because of Symmetry…
It stands to reason that the time it takes for
the object to travel up EQUALS
The time it takes for the object to travel
down.
If you want the object to go higher, what
must you do? How does that change the
total time for the trip?
Because of Symmetry…
The total time = 4 s
So, the time for the
trip up is 2 s and the
trip down is also 2 s
What does that mean for your stomp
rockets?
Look at the data table.
Calculate how high the highest stomp rocket
went?
What is the main reason one rocket goes
higher than another?