Accelerated Motion

1
Accelerated Motion

• Velocity, acceleration and gravity

2
How fast do things fall
3
Reflexes
4
Position-Time Graphs
1
2
3
4
5
Velocity v. Time
6
Definitions

• Velocity
• Change in position with respect to time
• v ?d/?t
• Which can be written as
• (dfinal-dinitial)/(tfinal-tinitial)
• Common notation
• (dfdi)/(tfti)

• Acceleration
• Change in velocity with respect to time
• a ?v/?t
• Which can be written as
• (vfinal-vinitial)/(tfinal-tinitial)
• Common notation
• (vfvi)/(tfti)

7
Velocity to Acceleration

• v?d/?t(dfinaldinitial)/(tfinaltinitial)
• a?v/?t(vfinalvinitial)/(tfinaltinitial)

8
(No Transcript)
9
Average Acceleration

• a ?v/?t(vfinalvinitial)/(tfinaltinitial)
• f final
• i initial
• If tinitial 0
• a (vfinal vinitial)/tfinal
• Or
• vf vi atf

10
Positive and Negative Acceleration
11
Practice Problem

• A soccer player is running at a constant velocity
  of 50.0km/h (31mph). The player falls and skids
  to a halt in 4.0 seconds.
• What is the average acceleration of the player
  during the skid?
• What is the plot of the velocity vs. time?

12
Practice Problem

• A water balloon in the sling of a water balloon
  launcher undergoes a constant acceleration
  25m/s2 for 1.5s.
• What is the velocity of the water balloon right
  after launch?

13
Practice Problem

• A car accelerates from rest at 5 m/s2 for 5
  seconds. It moves with a constant velocity for
  some time, and then decelerates at 5 m/s2 to come
  to rest. The entire journey takes 25 seconds.
  Plot the velocity-time graph of the motion.

14
Practice Problem
Determine the accelerations for a1, a2, a3, and
a4 for each time interval.
a1 4/5 a2 (4-4)/(10-5) a3 (16-4)/(20-10) a4
(0-16)/(30-20)
15
Frictionless Cars
16
Frictionless Car Plots
17
Good Reading on Plot
18
Velocity with Constant Acceleration

• Given
• Solve
• for tf
• Substitute in
• Yeilds

19
Velocity with Constant Acceleration

• Solve for vf

2
½
2
1
1
½
2
2
1
2
1
2
2
2
2
2
2
2
2
2
2
2
2
2
20
Graphs

• Determine which equations provide the area under
  the graph. (let ti 0)

(vf-vi)
(tf-ti)
½
1)
Velocity (m/s)
2
2)
tf
a
½
3)
(vf-vi)
2
1
(tf-ti)
(tf-ti)
2
Time (s)
21
Velocity with Constant Acceleration

• Equation to remember
• vf2 vi2 2a(df-di)

22
Position with Average Acceleration

• ?d/?t ?v ½ a ?t
• ?d ?v?t ½ a ?t2
• When ti 0
• df - di vitf ½ atf2

23
Position with Average Acceleration

• Equation to remember
• Final position initial position (change in
  velocity)time ½ (acceleration)(time squared)
• df di (vf-vi)t ½ at2

24
Table 3-3 Page 68

• Equations of Motion for Uniform Acceleration

Equation Variables Initial Conditions
Average Acceleration tf,vf,a vi
Velocity with Constant Acceleration tf,df,a di,vi
Position with Average Acceleration df,vf,a di,vi
25
Free Fall on the Moon
26
Free Fall on the Moon
27
Group Project pg 78

• How fast is the Earth spinning?
• 0.5 km/sec   
• How fast is the Earth revolving around the Sun?
• 30 km/sec   
• How fast is the Solar System moving around the
  Milky Way Galaxy?
• 250 km/sec   
• How fast is our Milky Way Galaxy moving in the
  Local Group of galaxies?
• 370 km/sec

28
Free Fall

• All Objects fall at the same speed regardless of
  mass (if you can neglect wind resistance).

29
Free Fall

• A ball or a bullet?
• .
• .

Position with Average Acceleration
Height with constant gravity
30
Falling
31
Poor little guy
32
Graphs
33
Cart Movement
34
Practice Problems

• If you throw a ball straight upward, it will rise
  into the air and then fall back down toward the
  ground.
• Imagine that you throw the ball with an initial
  velocity of 10.0 m/s.
• a. How long does it take the ball to reach the
  top of its motion?
• b. How far will the ball rise before it begins to
  fall?
• c. What is its average velocity during this
  period?

35
a. How long does it take the ball to reach the
top of its motion?
36
b. How far will the ball rise before it begins to
fall?
37
c. What is its average velocity during this
period?
38
Practice Problem

• A sudden gust of wind increases the velocity of a
  sailboat relative to the water surface from 3.0
  m/s to 5.5 m/s over a period of 60.0 s.
• a. What is the average acceleration of the
  sailboat?
• b. How far does the sailboat travel during the
  period of acceleration?

39
a. What is the average acceleration of the
sailboat?
40
b. How far does the sailboat travel during the
period of acceleration?
41
Practice Problem

• A car starts from rest with an acceleration of
  4.82 m/s2 at the instant when a second car
  moving with a velocity of 44.7 m/s (100mph by the
  way) passes it in a parallel line. How far does
  the first car move before it overtakes the second
  car?
• Setup an equation or graph

42
Setup the equation
0
0
43
(No Transcript)
44
Positiond
45
Velocityv?d/?t
46
Accelerationa?v/?t
47
(No Transcript)
48
(No Transcript)