1. Acceleration and Free Fall

2. What is acceleration?
Acceleration measures the rate of change in velocity.
Average acceleration = change in velocity/ time required for change

3. Units for acceleration

4. Sign is very important! Acceleration has both direction and magnitude
A negative value for acceleration does not always mean an object is slowing down!!

5. Acceleration
Increasing speed and decreasing speed should not be confused with the directions of velocity and acceleration:
Speeding up, moving to the right
Slowing down, moving to the right
Slowing down, moving to the left
Speeding up, moving to the left

6. Fill in the Chart Initial Velocity Acceleration Motion + - - or +
Speeding up, moving right/up -
Speeding up, moving left/down
Slowing Down moving right/up
Slowing Down, moving left/down
- or +
Constant Velocity
Speeding up from rest
Remaining at rest

7. Graph of Velocity vs Time
Question: What does the slope of this graph give you?
Answer: ACCELERATION
Rise = Δv
Run Δt
Vf – VAVG = Δv
tf – ti = Δt

8. The Kinematic Equations
You are going to loooooove these! 

9. Motion with constant acceleration
Kinematic Equations
The relationships between displacement, velocity and constant acceleration are expressed by equations that apply to any object moving with constant acceleration.

10. Displacement with constant acceleration
Δx = displacement
Vi = initial velocity
Vf = final velocity
Δt = time interval

11. Example: #1
A car accelerates uniformly from rest to a speed of 23.7 km/h in 6.5 s. Find the distance the car travels during this time.
Δx = displacement= distance= ?
Vi = initial velocity = rest = 0 km/h
Vf = final velocity = 23.7 km/h
Δt = time interval = 6.5 s
Look at final velocity…convert to m/s!!!

12. Problem Solving Final velocity conversion
Plug in values and solve for Δx

13. Velocity with constant uniform acceleration
Vf = final velocity
Vi = initial velocity
a = acceleration
Δt = time interval

14. Example: #2
An automobile with an initial speed of 4.30 m/s accelerates uniformly at the rate of 3.0 m/s2. Find the final speed after 5.0 seconds.
Vf = final velocity=?
Vi = initial velocity = 4.3 m/s
a = acceleration= 3.0 m/s2
Δt = time interval= 5.0 s

15. Solve
Plug in values and solve for Vf
Vf= 19 m/s

16. Displacement with constant uniform acceleration
Δx = displacement
Vi = initial velocity
a = acceleration
Δt = time interval

17. Example: #3
An automobile with an initial speed of 4.30 m/s accelerates uniformly at the rate of 3.0 m/s2. Find the displacement after 5.0 seconds.
Δx = displacement=??
Vi = initial velocity= 4.30 m/s
a = acceleration= 3.0 m/s2
Δt = time interval= 5.0 s

18. Solve!
Plug in values and solve for displacement

19. Final Velocity after any displacement
Vf = final velocity
Vi = initial velocity
a = acceleration
Δx = displacement

20. Example: #4
A car accelerates uniformly in a straight line from rest at the rate of 2.3 m/s2. What is the speed of the car after it has traveled 55 m?
Vf = final velocity=??
Vi = initial velocity= rest= 0 m/s
a = acceleration= 2.3 m/s2
Δx = displacement= 55 m

21. Solve

22. Rearranging
Your problems won’t always be so straightforward…make sure to rearrange your equations to solve for the unknown before plugging in your numbers (with units!)

23. Section 2-3 Falling Objects
Free Fall: Neglecting air resistance, all objects fall with the same constant acceleration
An object in free-fall is only subject to the force of gravity (weight)

24. Free Fall clips https://www.youtube.com/watch?v=V6xqgWVgAok

25. Acceleration due to gravity

26. Free Fall Acceleration
However, acceleration is a vector.
Gravity acts toward the earth (down)
Therefore, the acceleration of objects in free fall near the surface of the earth is

27. What we see because of air resistance…

28. Which object hits the ground first? (ignore air friction)
Which object hits the ground first when we include air friction?

29. No Air Resistance
With Air Resistance

30. Object falling from rest

31. All objects, when thrown up will continue to move upward for some time, stop momentarily at the peak, and then change direction and begin to fall.

32. Path of a projectile
At top of path
v= 0 m/s
a = m/s2

33. Free Fall Acceleration
At the highest point of an arc, an object has velocity = 0 m/s, acceleration is still m/s2
An object thrown into the air is a freely falling body with

34. Terminal Velocity?
Well, eventually, the force of air resistance becomes large enough to balance the force of gravity. At this instant in time the object stops accelerating. The object is said to have "reached a terminal velocity."

35. In situations in which there is air resistance, massive objects fall faster than less massive objects. Why?
Massive objects fall faster than less massive objects because they are acted upon by a larger force of gravity; for this reason, they accelerate to higher speeds until the air resistance force equals their gravity force.
Basically the more massive object accelerates longer before reaching terminal velocity.

36. Free Fall Problem
A flowerpot falls from a windowsill 25.0 m above the sidewalk
A. How fast is the flowerpot moving when it strikes the ground?
B. How much time does a paserby on the sidewalk below have to move out of the way before the flowerpot hits the ground?

37. Part. A. What are we looking for: Vf What do we know?
Displacement: -25 m
Acceleration: m/s2
Vi=0 m/s
What equation should we use??

38. Solve the problem 

39. Part b. How much time before the flowerpot hits the ground?
What do we know?
Displacement= m
Acceleration = m/s2
V initial= 0
V final = m/s
What are we looking for: Time!
Which equation should we use??

40. Solve the Problem 