1. 9/23 do now – on a new sheet
Which of the following is the expression for average velocity?
Homework questions?

2. Motion in one dimension
2.2
Acceleration

3. Lesson Objectives:
Describe motion in terms of changing velocity.
Compare graphical representations of accelerated and nonaccelerated motions.
Apply kinematic equations to calculate distance, time, or velocity under conditions of constant acceleration.

4. Do Now - Notes Key terms and ideas notes Acceleration def.
Acceleration direction
Graph representation
Equations

5. Acceleration Acceleration Acceleration is a Vector quantity
change in VELOCITY occuring over TIME
Acceleration = (change in velocity) / time
Acceleration is a Vector quantity
The unit for acceleration is
m/s2
Questions:
“If an object has a large velocity, does it necessarily have a large acceleration?
If an object has a large acceleration, does it necessarily have a large velocity?”

6. What are the three ways to accelerate your car?
Anytime an object's velocity is changing, the object is said to be accelerating; it has an acceleration.
What are the three ways to accelerate your car?
Gas pedal, break, steering wheel

7. Example – finding time of acceleration
A shuttle bus slows to a stop with an average acceleration of -1.8 m/s2. How long does it take the bus to slow from 9.0 m/s to 0.0 m/s?

8. Example – finding time of acceleration
Find the acceleration of an amusement park ride that falls from rest to a speed of 28 m/s in 3.0 s.

9. Do now
In addition to displacement, which of the following must be used for a more complete description of the average velocity of an object?
finish Class work Page 49 #1-5

10. The Direction of the Acceleration Vector
Negative Velocity
Negative Velocity
Positive Velocity
Positive Velocity
Negative Acceleration
Negative Acceleration
Positive Acceleration
Positive Acceleration
Slowing down
Eventually speeds up in + direction!
Slowing down
Eventually speeds up in – direction!
Speeding up in + direction
Speeding up in - direction

11. The Direction of the Acceleration Vector
demo
The Direction of the Acceleration Vector
The direction of the acceleration vector depends on whether the object is speeding up or slowing down
If an object is speeding up, then its acceleration is in the same direction of its motion.
moving in the + direction, the acceleration + direction
moving in the - direction, the acceleration - direction
If an object is slowing down, then its acceleration is in the opposite direction of its motion.
moving in the + direction, the acceleration - direction
moving in the - direction, the acceleration + direction
The direction of velocity and acceleration do not have to be the same!!!

12. The car will… The car will… The car will… The car will… +v -v +v -v +a
Conceptual challenge
Page 50

13. The slope of the v-t graph describe the object’s acceleration
Figure 2-10 B C
What is the Acceleration at A, B, C, D? A D
A: +10 m/s2
B: zero
C: -5 m/s2
D:-15 m/s2
What is happening at point D?

14. Conceptual challenge
Page 50

15. Constant acceleration
demo
Constant acceleration - the velocity is changing by a constant amount - in each second of time.

16. = vf + vi 2 ∆x ∆t ∆x = ½ (∆t)(vf + vi)
a = slope
∆x = ½ (∆t)(vf + vi)
The displacement equals to the area under the velocity vs. time graph

17. Determining the Area on a v-t Graph
In velocity versus time graphs, the area bounded by the line and the axes represents the displacement.

18. The shaded area is representative of the displacement
area = base x height
area = ½ base x height
area = ½ base x ( height1 + height2) or
area = big triangle – small triangle

19. example
Determine the displacement of the object during the time interval from 2 to 3 seconds (Practice A) and during the first 2 seconds (Practice B).
25 m
40 m

20. Example – 2C
A racing car reaches a speed of 42 m/s. It then begins a uniform negative acceleration, using its parachute and breaking system, and comes to rest 5.5 s later. Find how far the car moves before stopping.
120 m

21. Class work
Page 53 – practice 2C

22. Do now
Velocity measures all of the following EXCEPT a. the speed of an object. b. the total displacement of an object. c. the direction of an object’s motion. d. the displacement for each time interval.

23. Lesson Objectives:
Describe motion in terms of changing velocity.
Compare graphical representations of accelerated and nonaccelerated motions.
Apply kinematic equations to calculate distance, time, or velocity under conditions of constant acceleration.
Homework:
Castle learning
Must show work for incorrect answer after one try on a separate paper
Show name of assignment

24. Constant motion vs. accelerated motion ticker tape
constant velocity: displacement is changing by a constant amount - in each second of time.
constant acceleration: displacement is increasing in each second of time. Velocity is changing by a constant amount - in each second of time

25. Constant motion vs. accelerated motion vector diagrams

26. When velocity is constant
displacement vs. time (constant motion)
displacement
displacement
time
time
Constant, positive velocity
At rest
Constant motion - constant speed with constant direction
Slope represent velocity
Alert: in displacement vs. time graph, displacement can be positive or negative

27. velocity vs. time (constant motion)
Constant, positive velocity, zero acceleration
Constant negative velocity, zero acceleration
Slope represent acceleration
Alert: in velocity vs. time graph, velocity can be positive or negative

28. When velocity is changing
displacement vs. time (accelerated motion)
displacement
time
displacement
Slowing down in positive direction
Speeding up in positive direction
time
displacement
time
displacement
time
Slowing down in negative direction
Speeding up in negative direction

29. velocity vs. time (constant accelerated motion)
Speeding up in positive direction at constant rate
Acceleration is constant, positive
Slowing down in positive direction at constant rate, acceleration is constant, negative
velocity
time
velocity
time
velocity
velocity
time
time
Speeding up in negative direction at constant rate
Acceleration is constant, negative
Slowing down in negative direction at constant rate, acceleration is constant, positive

30. Alert – v vs. t and d vs. t must match
velocity
time
Disp.
time
Disp.
time
velocity
time
velocity
velocity
time
Disp.
time
Disp.
time
time

31. Determine acceleration - Example 1
From 0 s to 4 s:
From 4 s to 8 s:
0 m/s2
2 m/s2

32. Do now
Sketch displacement vs. time and velocity vs. time graphs to indicate an object is accelerating at a constant rate.

33. Lesson Objectives:
Describe motion in terms of changing velocity.
Compare graphical representations of accelerated and nonaccelerated motions.
Apply kinematic equations to calculate distance, time, or velocity under conditions of constant acceleration.

34. review Key terms and ideas notes Acceleration def.
Acceleration direction
Graph representation
Equations
Speed up: a and v have same sign
Slow down: a and v have opp. Sign
acc. = slope
disp = area v d v d
vavg
No acc.
No acc. t t t t

35. Final velocity depends on initial velocity, acceleration, and time

37. v vf vi t tf
In velocity versus time graphs, the area bounded by the line and the axes represents the displacement.

38. Example 2D
A plane starting at rest at one end of a runway undergoes a uniform acceleration of 4.8 m/s2 for 15 s before takeoff. What is the its speed at takeoff? How long must the runway be for the plane to be able to take off?

39. Class work
Page 55, practice 2D

40. Time and be found from displacement and velocity
Solve for ∆t
Sub ∆t in this equation

41. Example – 2E
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 4.75 m?

42. Class work
Page 58 – practice 2E #1-6

43. In one dimensional motion:
∆x = d

44. Class work
Section Review Worksheet 2-2

45. Do now
A car travels 90. meters due north in 15 seconds. Then the car turns around and travels 40. meters due south in 5.0 seconds. What is the magnitude of the average speed and average velocity of the car during this 20.-second interval?

46. Describe motion in terms of changing velocity.
Objectives - review
Describe motion in terms of changing velocity.
Compare graphical representations of accelerated and non accelerated motions.
Apply kinematics equations to calculate distance, time, or velocity under conditions of constant acceleration.
Homework
Castle learning, must show work for incorrect answers to get full credit

47. In one dimensional motion:
∆x = d

48. Example
A bicyclist accelerates from 5.0 m/s to a velocity of 16 m/s in 8 s. Assuming uniform acceleration, what displacement does the bicyclist travel during this time interval?
∆x = ½ (vf + vi)(∆t)
84 m

49. Example
A train starts from rest and leaves Greenburg station and travels for 500. meters with an acceleration of 1.20 meters per second2.
What is the train’s final velocity?
How long does it take the train to reach its final velocity?
vf2 = vi2 + 2ad
vf2 = 0 + 2(1.20 m/s2)(500. m)
vf = 34.6 m/s
vf = vi + at
34.6 m/s = 0 + (1.20 m/s2) t
t = 28.8 s

50. Example
A driver traveling at 85. miles per hour sees a police car hiding in the trees 2.00 miles ahead. He applies his brakes, decelerating at miles per hour2.
If the speed limit is 55 mph, will he get a ticket?
What would his acceleration need to be to not get a ticket?
vf2 = vi2 + 2ad
vf2 = (85. mph)2 + 2(-500. mph2)(2.00 mi)
vf = 72.3 mph *YES*
vf2 = vi2 + 2ad
(55 mph)2 = (85. mph)2 + 2a(2.00 mi)
a = mph2

51. Class work
Problem workbook 2A, 2B, 2C, 2D, 2E