Reminders

1
Reminders

• plots of position vs. time that linearly
  increase cannot give rise to velocity vs. time
  curves that linearly increase.

v
t
2
Reminders

• plots of velocity vs. time that linearly
  increase cannot give rise to acceleration vs.
  time curves that linearly increase.

a
t
3
Reminders

• acceleration links to changing velocity
• changing velocity links to curved position vs.
  time plots

v
x
t
t
4
Kinematics How Things Move in 1D
Points to take away

• There are several useful equations that we can
  use to describe motion with constant
  acceleration.
• The most common application of them is to
  describe the motion of objects in free-fall,
  motion under the influence of gravity near the
  surface of the Earth.

5
Linear Motion

• When we are dealing with 1-dimensional linear
  motion, dealing with vectors is easy there is
  only one direction (our reference frame only has
  one axis) and motion is either in the positive or
  negative direction.

y
z
x
-x
-z
-y
6
Kinematic Equations

• average velocity and displacement (true even if
  a is not constant)

avg. velocity is the slope of a position vs. time
curve
(xf-xi)/(tf-ti)
xf xi (tf-ti)

• average velocity (true only if a is constant)

(vfvi)/2

• average acceleration (true only if a is constant)

a (vf-vi)/(tf-ti)
avg. acceleration is the slope of a velocity vs.
time curve
vf vi (tf-ti)
7
Kinematic Equations

• These basic definitions can be combined to form
  additional equations (only for constant
  acceleration!)
• xf xi vi ?t ½ a (?t)2
• vf2 vi2 2a (xf xi)
• Use units to help you!

8
Example

• A car is traveling at 40 km/h when a kid runs
  into the road 13 m ahead. The driver applies the
  brakes, which produce an acceleration of -8.0
  m/s2. If the drivers reaction time is 0.25 s,
  will the kid be hit?

9
Acceleration Due to Gravity
Racquetball vs. Paper
Hammer vs. Feather

• Racquetball wins
• Paper is light, like air, so it wants to stay in
  the air
• Is this really free fall?

• Its a tie!
• In true free fall, like on the Moon, all objects
  are accelerated equally

10
2 Person Discussion

• Do I have to release an object from rest (zero
  velocity) for it to be in free fall? Why or why
  not?
• If I throw a ball straight down, is the
  acceleration due to gravity larger or smaller
  than if I released it from rest? Why?
• If I throw a ball straight up, what is its
  velocity when it reaches its maximum height?
  What is the acceleration due to gravity at that
  point? Why?

11
Example

• Susie throws a rock downward from a bridge with
  a speed of 14.7 m/s. If she hears the splash
  2.00 s later, how high is the bridge above the
  water? How fast is the rock going when it hits
  the water?

12
NEXT

• Sections 3.1 3.2 2-D Motion
• 2-D vectors
• components
• adding subtracting vectors in 2-D

13
2 Minute Quiz 1

• A train moves along a straight track. The graph
  at right shows the position of the train as a
  function of time. The graph shows that the train
• always speeds up
• always slows down
• speeds up sometimes, slows down sometimes
• has a constant speed

position
time
14
2 Minute Quiz 2
A

• 2 trains run on parallel tracks. From the
  graph on the right, which is true?
• At time tB, both trains have the same velocity.
• Both trains speed up always.
• Both trains have the same velocity at some time
  before tB
• Both trains have the same acceleration somewhere
  on the graph.

B
position
time
tB