Final Velocity after Any
Displacement
The Last Equation…
For now
The Last Equation
• If we take the equations that we’ve looked at
so far, and do some mathematical hand
waving…
• We get:
vf
2
2
 vi  2 a  x
Example
• A person pushing a stroller starts from rest, uniformly
accelerating at a rate of 0.500 m/s2. What is the velocity of
the stroller after it has traveled 4.75m?
Example
• A person pushing a stroller starts from rest, uniformly
accelerating at a rate of 0.500 m/s2. What is the velocity of
the stroller after it has traveled 4.75m?
• Givens: a= 0.500 m/s2 vi= 0 m/s
Δx=4.75 m vf= ?
Example
• A person pushing a stroller starts from rest, uniformly
accelerating at a rate of 0.500 m/s2. What is the velocity of
the stroller after it has traveled 4.75m?
• Givens: a= 0.500 m/s2 vi= 0 m/s
Δx=4.75 m vf= ?
vf
2
2
 vi  2 a  x
Example
• A person pushing a stroller starts from rest, uniformly
accelerating at a rate of 0.500 m/s2. What is the velocity of
the stroller after it has traveled 4.75m?
• Givens: a= 0.500 m/s2 vi= 0 m/s
Δx=4.75 m vf= ?
vf
vf
vf
2
 vi  2 a  x
2
2
 ( 0 m / s )  2 ( 0 . 500 m / s )( 4 . 75 m )
2
 4 . 75 m / s
2
vf 
2
2
2
2
4 . 75 m / s
2
 2 . 18 m / s
Practice
• Pg. 58 Practice E
Falling Objects
vf
2
2
 vi  2 a  y
Same Equation, Different
Direction
A new given…
• When an object falls straight down it is in Free
Fall.
• Objects in Free Fall always have the same
acceleration- the acceleration of gravity (g).
• a= -9.8 m/s2 (this will ALWAYS be ‘a’ for a
‘falling’ object- either thrown up or falling
down)
Positive and Negative
• Variables that are Negative are in the
Downward direction.
• Variables that are Positive are in the Upward
direction.
a= -9.8m/s2
-Δy
Example
• Jason hits a volleyball so that it moves with an initial
velocity of 6.0 m/s straight upward. If the volleyball starts
from 2.0m above the floor, how long will it be in the air
before it strikes the floor?
Example
• Jason hits a volleyball so that it moves with an initial
velocity of 6.0 m/s straight upward. If the volleyball starts
from 2.0m above the floor, how long will it be in the air
before it strikes the floor?
• Givens: a=-9.8m/s2
vi=6.0m/s
Δy= -2.0m
t=?
Example
• Jason hits a volleyball so that it moves with an initial
velocity of 6.0 m/s straight upward. If the volleyball starts
from 2.0m above the floor, how long will it be in the air
before it strikes the floor?
• Givens: a=-9.8m/s2
vi=6.0m/s
Δy= -2.0m
t=?
v f  v i  at
vf
2
2
 vi  2 a  y
We can’t solve for t right away, so
use a 2-step process.
Step1- Find vf
Step 2- Find t
Practice
• Pg 63, Practice F