1. Final Velocity after Any Displacement
The Last Equation…
For now

2. The Last Equation
If we take the equations that we’ve looked at so far, and do some mathematical hand waving…
We get:

3. Example
A person pushing a stroller starts from rest, uniformly accelerating at a rate of m/s2. What is the velocity of the stroller after it has traveled 4.75m?

4. Example
A person pushing a stroller starts from rest, uniformly accelerating at a rate of m/s2. What is the velocity of the stroller after it has traveled 4.75m?
Givens: a= m/s2 vi= 0 m/s Δx=4.75 m vf= ?

5. Example
A person pushing a stroller starts from rest, uniformly accelerating at a rate of m/s2. What is the velocity of the stroller after it has traveled 4.75m?
Givens: a= m/s2 vi= 0 m/s Δx=4.75 m vf= ?

6. Example
A person pushing a stroller starts from rest, uniformly accelerating at a rate of m/s2. What is the velocity of the stroller after it has traveled 4.75m?
Givens: a= m/s2 vi= 0 m/s Δx=4.75 m vf= ?

7. Practice
Pg. 58 Practice E

8. Falling Objects Same Equation, Different Direction

9. 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)

10. 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

11. 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?

12. 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=?

13. 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=?
We can’t solve for t right away, so use a 2-step process.
Step1- Find vf
Step 2- Find t

14. Practice
Pg 63, Practice F