Physics 2211: Lecture 3 Agenda for Today

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Physics 2211 Lecture 3Agenda for Today

• More Linear Motion (1-D Kinematics)
• Constant acceleration
• Free fall

2
Review

• For constant acceleration we find

x
t
v
t
a
t
3
Derivation

• Plugging in for t

4
Average Velocity

• Remember that

v
v
vav
v0
t
t
5
Recap

• For constant acceleration

• From which we know

6
Problem 1

• A car is traveling with an initial velocity v0.
  At t 0, the driver puts on the brakes, which
  slows the car at a rate of ab

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Problem 1...

• A car is traveling with an initial velocity v0.
  At t 0, the driver puts on the brakes, which
  slows the car at a rate of ab. At what time tf
  does the car stop, and how much farther xf does
  it travel?

v0
ab
x 0, t 0
v 0
x xf , t tf
8
Problem 1...

• Above, we derived v v0 at
• Realize that a -ab
• Also realizing that v 0 at t tf
• find 0 v0 - ab tf or
• tf v0 /ab

9
Problem 1...

• To find stopping distance we use

• In this case v vf 0, x0 0 and x xf

10
Problem 1...

• So we found that
• Suppose that vo 65 mi/hr 29 m/s
• Suppose also that ab g 9.81 m/s2
• Find that tf 3 s and xf 43 m

11
Recap

• For constant acceleration we found

x
t
v

• From which we derived

t
a
t
12
1-D Free-Fall

• This is a nice example of constant acceleration
  (gravity)
• In this case, acceleration is caused by the force
  of gravity
• Usually pick y-axis upward
• Acceleration of gravity is down

y
t
v
t
a
y
t
ay ? g
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Gravity facts

• g does not depend on the nature of the material!
• Galileo (1564-1642) figured this out without
  fancy clocks rulers!
• Nominally, g 9.81 m/s2
• At the equator g 9.78 m/s2
• At the North pole g 9.83 m/s2
• More on gravity in a few lectures!

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Lecture 3, Act 1D free fall

• Alice and Bill are standing at the top of a cliff
  of height H. Both throw a ball with initial
  speed v0, Alice straight down and Bill straight
  up. The speed of the balls when they hit the
  ground are vA and vB respectively. Which of the
  following is true
• (a) vA lt vB (b) vA vB (c) vA gt
  vB

v0
Bill
Alice
v0
H
vA
vB
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Problem 2

• The pilot of a hovering helicopter drops a lead
  brick from a height of 1000 m. How long does it
  take to reach the ground and how fast is it
  moving when it gets there? (neglect air
  resistance)

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Problem 2

• First choose coordinate system.
• Origin and y-direction.
• Next write down position equation
• Realize that v0y 0.

1000 m
y 0
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Problem 2

• Solve for time t when y 0 given that y0 1000
  m.
• Recall
• Solve for vy

y0 1000 m
y 0
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Tips

• Read !
• Before you start work on a problem, read the
  problem statement thoroughly. Make sure you
  understand what information is given, what is
  asked for, and the meaning of all the terms used
  in stating the problem.
• Watch your units !
• Always check the units of your answer, and carry
  the units along with your numbers during the
  calculation.
• Understand the limits !
• Many equations we use are special cases of more
  general laws. Understanding how they are derived
  will help you recognize their limitations (for
  example, constant acceleration).

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Recap of todays lecture

• More 1-D Kinematics (Chapter 2)
• Motion with constant acceleration free fall
  
• Act, Examples
• For next time Read 3-1, 3-2 in Tipler.