Motion

1
Motion
2
Motion

• Change in position with respect to change in time

3
Position

• The separation from the origin

4
Position Time
5
Position-Time Graph
6
Position-Time Graph (2)
7
Average Velocity

• Average velocity is the change in position
  (displacement) divided by the time interval
  during which the displacement took place. If you
  know two of the three quantities in this
  relationship, you can determine the third
  mathematically.

8
Average Velocity

• 1. A car travels at 55 km/h for 6.0 hours. How
  far does it travel?
• 2. A missile travels 2500 km in 2.2 hours. What
  is its velocity?
• 3. How many minutes will it take a runner to
  finish an 11-km race at 18 km/h?

9
Average Velocity

• 5. A businesswoman on a trip flies a total of
  23,000 km. The first day she traveled 4000 km,
  the second day 11,000 km, and on the final day
  she was on a plane that could travel at 570 km/h.
  How long was she on the plane the final day?

10
Instantaneous Velocity

• The velocity at a single point in time.

11
Instantaneous Velocity

• 1. Many cars require an oil change every
  40005000 km. If this car travels without a break
  for 4800 km at 120 km/h, how long will it take to
  simulate one full cycle of time without an oil
  change?
• 2. Some cars have a warranty that lasts for up to
  150,000 km. How long would it take for the
  warranty to run out if the car ran constantly at
  110 km/h?

12
Instantaneous Velocity

• 3. A car is tested for 1800 km on one day, 2100
  km another day, and then is driven 65 km/h for 72
  hours. What is the total distance the car has
  traveled?
• 4. The odometer on a car reads 4100 km after 3
  days of tests. If the car had been tested on one
  day for 1500 km, a second day for 1200 km, then
  how long was the car tested the last day if it
  traveled at 120 km/h while being tested?

13
Instantaneous Velocity

• 5. Car A traveled 1200 km in 8.0 h. Car B
  traveled 1100 km in 6.5 h. Car C traveled 1300 km
  in 8.3 h. Which car had the highest average
  velocity. How long would it have taken the
  slowest car to travel the same distance as the
  fastest car?
• 6. One car tested can travel 780 km on a tank of
  gasoline. How long should the car be able to
  travel at 65 km/h before it runs out of gas? If
  the car has a 53-L tank, then what is the average
  mileage of the vehicle?

14
Instantaneous Velocity

• 7. Cars Q and Z are put through an endurance test
  to see if they can travel at 120 km/h for 5.0
  hours. Each car has a 45-L fuel tank. Car Z must
  stop to refuel after traveling for 4.2 hours. Car
  Q, however, travels for 5.4 hours before running
  out of gas. For each car, calculate the average
  kilometers traveled for each liter of gas (km/L).

15
Instantaneous Velocity

• 8. Refer to the problem above. How many liters
  does Car Q have left in its fuel tank after
  traveling for five hours at 120 km/h? If you were
  to test-drive Car Q across a desert where there
  were no fuel stations available for 1200 km, how
  many 10-L gas cans should you have in the car to
  refuel along the way?

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Motion Diagram
17

• Vector
• A quantity that has both magnitude and direction
• 3m South (-3y)

• Scalar
• A quantity that has only magnitude
• 3m

18
Velocity vs. Speed

• Velocity
• Total displacement
• (change in position) with
• respect to total time

• Speed
• Total distance traveled
• with respect to total time

19
Motion Diagram
20
Vector Addition
21
Vector Addition
22
Vector Subtraction
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Vector Addition

• Tail to Tip

24

Vector Addition
Total distance 7m Time elapsed
7s X 4m Y
3m Total displacement sqrt(42
32)5m (a2b2c2)
y
3
2
Velocity 5m/7s 0.7m/s Speed 7m/7s 1m/s
1
x
3
1
2
4
(one second per block)
25
Practice Problem

• Joe goes for a run. From his house, he jogs north
  for exactly 5.00h at an average speed of 10.0
  km/h. He continues north at a speed of 10.0 km/h
  for the next 30.0h. He then turns around and jogs
  south at a speed of 15.0 km/h for 15.0h. Then he
  jogs south for another 20.0h at 5.00 km/h. He
  walks the rest of the way home.
• How many kilometers does Joe jog in total?
• How far will Joe have to walk to get home after
  he finishes jogging?

26
Practice

• 1. An airplane travels at a constant speed,
  relative to the ground, of 900.0 km/h.
• a. How far has the airplane traveled after 2.0 h
  in the air?
• b. How long does it take for the airplane to
  travel between City A and City B if the cities
  are 3240 km apart?
• c. If a second plane leaves 1 h after the first,
  and travels at 1200 km/h, which flight will
  arrive at City B first?
• 2. You and your friend start jogging around a
  2.00x103-m running track at the same time. Your
  average running speed is 3.15 m/s, while your
  friend runs at 3.36 m/s. How long does your
  friend wait for you at the finish line?

27
Practice

• 3. The graph shows the distance versus time for
  two cars traveling on a straight highway.
• a. What can you determine about the relative
  direction of travel of the cars?
• b. At what time do they pass one another?
• c. Which car is traveling faster? Explain.
• d. What is the speed of the slower car?

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Practice

• 4. You drop a ball from a height of 2.0 m. It
  falls to the floor, bounces straight upward 1.3
  m, falls to the floor again, and bounces 0.7 m.
• a. Use vector arrows to show the motion of the
  ball.
• b. At the top of the second bounce, what is the
  total distance that the ball has traveled?
• c. At the top of the second bounce, what is the
  balls displacement from its starting point?
• d. At the top of the second bounce, what is the
  balls displacement from the floor?

29
Practice

• 5. You are making a map of some of your favorite
  locations in town. The streets run northsouth
  and eastwest and the blocks are exactly 200 m
  long. As you map the locations, you walk three
  blocks north, four blocks east, one block north,
  one block west, and four blocks south.
• a. Draw a diagram to show your route.
• b. What is the total distance that you traveled
  while making the map?
• c. Use your diagram to determine your final
  displacement from your starting point.
• d. What vector will you follow to return to your
  starting point?

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Practice

• 6. An antelope can run 90.0 km/h. A cheetah can
  run 117 km/h for short distances. The cheetah,
  however, can maintain this speed only for 30.0 s
  before giving up the chase.
• a. Can an antelope with a 150.0-m lead outrun a
  cheetah?
• b. What is the closest that the antelope can
  allow a cheetah to approach and remain likely to
  escape?

31
Practice

• 7. The position-time graph to the right
  represents the motion of three people in an
  airport moving toward the same departure gate.
• a. Which person travels the farthest during the
  period shown?
• b. Which person travels fastest by riding a
  motorized cart? How can you tell?
• c. Which person starts closest to the departure
  gate?
• d. Which person appears to be going to the wrong
  gate?

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Practice

• 8. A radio signal takes 1.28 s to travel from a
  transmitter on the Moon to the surface of Earth.
  The radio waves travel at 3.00x108 m/s. What is
  the distance, in kilometers, from the Moon to
  Earth?

33
Practice

• 9. You start to walk toward your house eastward
  at a constant speed of 5.0 km/h. At the same
  time, your sister leaves your house, driving
  westward at a constant speed of 30.0 km/h. The
  total distance from your starting point to the
  house is 3.5 km.
• a. Draw a position-time graph that shows both
  your motion and your sisters motion.
• b. From the graph, determine how long you travel
  before you meet your sister.
• c. How far do you travel in that time?

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Practice

• 10. A bus travels on a northbound street for 20.0
  s at a constant velocity of 10.0 m/s. After
  stopping for 20.0 s, it travels at a constant
  velocity of 15.0 m/s for 30.0 s to the next stop,
  where it remains for 15.0 s. For the next 15.0 s,
  the bus continues north at 15.0 m/s.
• a. Construct a d-t graph of the motion of the
  bus.
• b. What is the total distance traveled?
• c. What is the average velocity of the bus for
  this period?

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Position vs. Time
36
Review 2.1

• 1. What is a motion diagram?
• A series of images showing the position of a
  moving object at equal time intervals.
• 2. How is a particle diagram different from a
  motion diagram? Which diagram is simpler?
• The particle model is a motion diagram in which
  the object has been replaced by a series of
  single points. The particle model is simpler than
  the motion diagram.
• 3. What are the two components used to define
  motion?
• Place and time
• 4. Give three examples of straight-line motion.
• Car, meteor, light

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Review 2.2

• 1. What is the primary difference between a
  scalar and a vector?
• A vector has both magnitude and direction, while
  a scalar only has magnitude.
• 2. What is a resultant?
• A resultant is the sum of two or more vectors.
• 3. A student walks 4 blocks north then stops for
  a rest. She then walks 9 more blocks north and
  rests, then finally another 6 blocks north. What
  is her displacement in blocks?
• ?d df- di
• If the students starting point is defined as
  zero, the equation
• becomes
• ?d df.
• Thus, the students displacement is equal to his
  or her final position and the
• final position is equal to the sum of all of the
  displacements. So,
• ?d d1d2d3
• ?d (4 blocks N)(9 blocks N)(6 blocks N) 19
  blocks N

38
Review 2.2

• 4. A runner runs 6 km east, 6 km north, 6 km
  west, and finally 6 km south. What is his total
  displacement? Draw a diagram.

6 km West
6 km South
6 km North
Starting Point
6 km East
39
Review 2.3

• 1. On a position-time graph, which of the two
  variables is on the x-axis? Which is on the
  y-axis?
• Time is represented on the x-axis and position is
  represented on the y-axis.
• 2. If the plotted line on a position-time graph
  is horizontal what does this indicate?
• The object the graph represents is not moving.
• 3. Can the plotted line on a position-time graph
  ever be vertical? Explain your answer.
• This is unlikely, as this would represent an
  object moving at an infinite speed.

40
Review 2.3

• 4. A position-time graph plots the course of two
  runners in a race. Their lines cross on the
  graph. What does this tell you about the
  runners?
• They are in the same place at the same time.
• 5. Does the intersecting line on a position-time
  graph mean that the two objects are in collision?
  Explain
• The objects are in the same place at the same
  time, but they are not necessarily in collision.
  All that is known is that their position with
  reference to the origin is the same.

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Review 2.4

• 1. What is the difference between speed and
  velocity?
• Speed does not contain a direction component and
  velocity does. In other words, speed is a scalar
  quantity and velocity is avector quantity.
• 2. What is the difference between average
  velocity and instantaneous velocity? Give an
  example of each.
• Average velocity is the total distance traveled
  divided by the total time of travel. An example
  of average velocity is a 120-mile car trip that
  takes 2 hours, average velocity was 60 mph.
• Instantaneous velocity is the velocity at one
  given instant. An example of instantaneous
  velocity is the velocity recorded by a police
  radar gun.
• 3. Define all three variables in the equation
  v?d/?t and indicate the appropriate label for
  each in SI terms.
• v is velocity in m/s,
• t is time in s,
• d is distance in m.

42
Review 2.4

• 4. What is the average velocity of a car that
  travels 450 km in 9.0 hours?
• v?d/?t
• 450km/9.0h 5.0x101
• 5. How far has a cyclist traveled if she has been
  moving at 30 m/s for 5.0 minutes?
• v?d/?t
• ?dv?t
• (30m/s)(3.0x102 s) 9000m

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Velocity vs. Time (Ch 3)