Motion in One Dimension

1
Chapter 2

• Motion in One Dimension

2
Displacement

• Measures the change in position
• Represented as ?x (if horizontal) or ?y (if
  vertical)
• Vector quantity
• or - is generally sufficient to indicate
  direction for one-dimensional motion

3
Displacements
4
Distance

• Distance is the magnitude of the displacement
  distance does not have direction
• Blue line shows the distance
• Red line shows the displacement

5
Velocity

• The average velocity is rate at which the
  displacement occurs
• The initial time is usually 0, so ti 0

6
Velocity continued

• Suppose a truck traveled from 10 m to 80 m in the
  positive direction in 5 seconds. What is the
  trucks velocity?
• Suppose the same truck, which is now located at
  80 m, wants to return 10 m west of its original
  location (its starting point). What is his
  velocity?

7
Position-time graphs (p.25) Slope of AD
velocity from A to D
8
Speed vs. Velocity

• Speed and velocity are different!
• Velocity can be either positive or negative,
  depending on the sign of the displacement. So if
  an object is moving in the negative direction,
  its velocity will be negative.
• Speed has no direction and therefore carries no
  sign.

9
Speed vs. Velocity

• A car is rounding the corner at a constant speed
  of 30 mi/h. Is its velocity constant?
• The average speed of an object is defined as
  total distance
• total time

10

• 1.) The world speed record on water was set on
  October 8, 1978 by Ken Warby of Blowering Dam,
  Australia. If Ken drove his motorboat a distance
  of 1000m in 7.045 seconds, how fast was his boat
  moving (a) in m/s? (b) in mi/h?

11

• 2.) May 29, 1988, Rick Mears won the Indianapolis
  500 in 3.45 hours. What was his average speed
  during the 500 mi-race
• 3.) The slowest animal ever discovered was a crab
  found in the Red Sea. It traveled with an
  average speed of 5.70 km/y. How long would it
  take this crab to travel 100km?

12
DO NOW 12/11/08

• Benjamin watches a thunderstorm from his
  apartment window. He sees the flash of a
  lightning bolt and begins counting the seconds
  until he hears the clap of thunder 10 seconds
  later. Assume the speed of sound in air is 340
  m/s. How far away was the lightning bolt (a) in
  m? (b) in km?
• NOTE The speed of light, 3.0 x 108 m/s, is
  considerably faster than the speed of sound.
  That is why you see the lightning flash so much
  earlier than you hear the clap of thunder. In
  actuality, the lightning and thunder clap occur
  almost simultaneously.

13
Instantaneous Velocity

• The slope of the line tangent to the
  position-time curve at one point.

14
p. 28 Example 2.1
15
Acceleration
16
Acceleration

• Acceleration is the rate of change of velocity
• A track runner starts a 10 minute race with a
  velocity of 3mi/hr. He accelerates to a
  velocity of 5mi/hr. What is his acceleration?

17
DO NOW 12/12

• If an object has a zero velocity, is its
  acceleration zero?
• Is it possible for an object to have a nonzero
  velocity but a zero acceleration?
• Create a position-time graph that illustrates
  each situation
• An object moves in a positive direction with a
  non-constant velocity
• An object moves in the negative direction with a
  constant velocity
• An object has no movement

18

• 1.) Suppose a car accelerates from an initial
  velocity of vi 10 m/s to a final velocity of
  vf 30 m/s in a time interval of 2.0 s. What
  is the cars acceleration?
• 2.) If the cars velocity went from 10m/s to
  5m/s in the same time interval, what would the
  acceleration be? Is the car speeding up or
  slowing down in this case?
• 3.) Suppose a car accelerates from an initial
  velocity of vi 8 m/s to a final velocity of
  vf 24 m/s in a time interval of 4.0 s. What
  is the cars acceleration?
• 4.) If the cars velocity went from 20 m/s to
  3 m/s in the same time interval, what would the
  acceleration be? Is the car speeding up or
  slowing down in this case?
• 5.) What conclusions can you make about the
  direction of the velocities and the acceleration?
  (How are they related?)

19

• When the objects velocity and acceleration are
  in the same direction, the speed of the object
  increases with time (speeding up). When the
  objects velocity and acceleration are in
  opposite directions, the speed of the object
  decreases with time (slowing down).
• P. 14 (a) (f)

20
Constant Acceleration

• When an object moves with constant acceleration,
  the instantaneous acceleration at any point in a
  time interval is equal to the value of the
  average acceleration over the entire time
  interval.

21
Equations to use when Acceleration is constant
22
v v0 at

• This equation can be used when you have an
  initial velocity, acceleration, and a time
  interval. For example A car starts with a
  velocity of 2.0 m/s to the right and accelerates
  to the right with a 6.0 m/s2, what will its
  velocity be after 2.0s have elapsed?

23
Constant Acceleration

• Average velocity (v0 v)
• 2
• ?x ½(v0 v)t
• When you are looking for displacement, given an
  initial and final velocity and time

24

• Gives displacement as a function of time, initial
  velocity and acceleration
• v2 v02 2a ?x
• Gives velocity as a function of displacement
•  

25
Free Fall

• Free falling objects are under the influence of
  gravity alone.
• The acceleration of a freely falling object is
  always 9.8 m/s2 at any time t. We can use the
  letter g to represent this acceleration in free
  fall. Therefore, g 9.8 m/s2
• An apple drops from a tree and hits the ground in
  8 seconds. How high above the ground was it when
  it first dropped?

26
Free Fall

• What happens when you throw a ball up? Does it
  gain speed or lose speed on the way up? Why?
• Does it gain speed or lose speed on the way down?
  Why?
• Is there a point in its motion where its velocity
  is zero?

27

• 1.) A car with an initial speed of 6.5 m/s
  accelerates at a uniform rate of 0.92 m/s2 for
  3.6 s. Find the final speed and the displacement
  of the car during this time.
• 2.) A car accelerates uniformly in a straight
  line from rest at the rate of 2.3 m/s2. (a) What
  is the speed of the car after it has traveled 55
  m? (b) How long does it take the car to travel 55
  m?

28

• 3.) A car accelerates uniformly from rest to a
  speed of 6.6 m/s in 6.5 s. Find the distance the
  car travels during this time.
• 4.) An automobile with an initial speed of 4.30
  m/s accelerates uniformly at the rate of
  3.00m/s2. Find the final speed and the
  displacement after 5.00s.
• 5.) A certain car is capable of accelerating at a
  uniform rate of 0.85 m/s2. What is the magnitude
  of the cars displacement as it accelerates
  uniformly from a speed of 83 km/h to one of 94
  km/h?