Motion

1
Chapter 2

• Motion

2
Describing Motion

• Motion is the change in position relative to a
  frame of reference.
• Frame of Reference The object or point from
  which movement is determined.
• Example When we say that a space shuttle moves 8
  km/sec, we mean that its movement relative to
  Earth below.
• When we say a racing car in the Indy 500 reaches
  a speed of 300 km/hr, of course we mean relative
  to the track.
• Unless stated otherwise, when we discuss the
  speeds of things in our environment, we mean
  speed with respect to the surface of the Earth.

3
Describing Motion

• Motion is measured by distance and time.
• Distance (d) How far an object moves.
• Time (t) Continuous period measured by clocks,
  watches, and calendars.
• Displacement (?x) is the distance and direction
  of an objects change in position from the
  starting point.
• Displacement Final Position Initial Position
• ?x xf - xi
• Displacement and distance are not the same thing.
• Example
• Suppose a runner jogs to the 50-m mark and then
  runs back to the 20-m mark.
• The runner travels a distance of 80-m (50-m
  30-m).
• The runner only displaces himself 20-m (20-m
  0-m).
• The only time distance and displacement are the
  same is if the motion was in a single direction.

4
Describing Motion

• Speed The distance traveled by a moving object
  per unit of time.
• Speed Distance/Time
• Units of Speed meters/second (m/s),
  kilometers/hour (km/hr), miles/hour (mph),
  feet/second (ft/s).
• Example
• A car traveling at a constant speed covers a
  distance of 750-m in 25-s. What is the cars
  speed?
• Speed Distance/Time
• Speed 750-m/25-s
• Speed 30-m/s

5
Describing Motion

• Examples
• A car travels 300-km in 6-hrs. What is the speed
  of the car?
• Speed 300-km/6-hrs
• Speed 50-km/hr
• What is the speed of a jet plane that flies
  7200-km in 9-hrs?
• Speed 7200-km/9-hrs
• Speed 800-km/hr
• The speed of a cruise ship is 50-km/hr. How far
  will the ship travel in 14-hrs?
• Speed Distance/Time
• 50-km/hr Distance/14-hrs
• Distance (50-km/hr) (14-hrs)
• Distance 700-km

6
Describing Motion

• Constant Speed Speed that does not change.
• The graph to the right shows the constant speed
  of a runner.
• Notice that a distance-time graph for constant
  speed is a straight line.
• Example
• What is the speed of the runner?
• Speed 50-m/5-s
• Speed 10-m/s

7
Describing Motion

• The slope of the distance-time graph is directly
  related to the speed.
• The steeper the slope, the faster the speed.
• Example
• What is the speeds of the swimmers in the graph
  to the right?
• Speed 1 100-m/50-s
• Speed 1 2-m/s
• Speed 2 50-m/50-s
• Speed 1-m/s

8
Describing Motion

• Usually speed is not constant.
• Average speed describes speed of motion when
  speed is changing.
• Average Speed The total distance traveled by the
  total time of travel.
• Average Speed Total Distance/Total Time
• The graph to the right is a graph of a cyclist
  that keeps changing speeds during the trip.
• Example
• If the rider in this graph covers a distance of
  5-km in 0.25 hours, what is the average speed?
• Average Speed 5-km/0.25-hrs
• Average Speed 20-km/hr

9
Describing Motion

• Example
• According to this distance-time graph, how far
  did the object move between the first and second
  hour?
• What was the average speed after one hour?
• What was the average speed after two hours?
• What was the average speed for the entire trip?

10
Describing Motion

• Instantaneous Speed is the speed at a given point
  in time.
• Example
• Your cars speedometer. A speedometer shows how
  fast a car is going at one point in time or at
  one instant.
• When something is speeding up or slowing down, it
  instantaneous speed is changing.
• The speed is different at every point in time.
• If an object is moving with constant speed, the
  instantaneous speed doesnt change. The speed is
  the same at every point in time.

11
Describing Motion

• As we have seen, the motion of an object over a
  time can be shown on a distance-time graph.
• Time is plotted on the horizontal axis and the
  distance traveled is plotted on the vertical
  axis.
• If the object moves with a constant speed, the
  increase in distance over equal time intervals is
  the same.
• This results in a straight line.

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Describing Motion

• Example
• Draw a distance-time graph for the following
  motion.
• Is this a graph for constant speed or changing
  speed?
• How do you know?
• What is the average speed for this trip?

13
Describing Motion

• Example
• Draw a distance-time graph for the following
  motion.
• Is this a graph for constant speed or changing
  speed?
• How do you know?
• What is the average speed for this trip?

14
Describing Motion

• Velocity is speed in a given direction.
• Velocity Displacement/Time
• Examples
• The speed of a hurricane is 20-km/hr.
• The velocity is 20-km/hr east.
• Why is a direction necessary?
• Navigation by land, sea, or air requires precise
  measurements of velocity (speed and direction).
• If a pilot wants to reach the Hawaiian Islands, a
  pilot must determine both the direction and speed
  of the plane.
• If either measurement is wrong, the plane will
  not reach its destination.

15
Describing Motion

• Because velocity depends on direction as well as
  speed, the velocity of an object can change even
  if the speed of the object remains constant.
• Example
• A race car traveling around a track at a constant
  speed.
• Even though the speed remains constant, the
  velocity changes because the direction of the
  cars motion is changing constantly.

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Describing Motion

• Examples
• A person walked a distance of 1.60-km east in
  30-minutes. What is the velocity of the person in
  kilometers per hour?
• Velocity 1.60-km/0.50-hrs
• Velocity 3.2km/hr East
• A car travels straight south for 200-miles in
  2.5-hours. What is the velocity of the car in
  miles per hour?
• Velocity 200-miles/2.5-hours
• Velocity 80-mi/hr South

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Acceleration

• Acceleration is the rate of change in velocity.
• When the velocity of an object changes, the
  object is accelerating.
• To calculate acceleration, divide the change in
  velocity by the time it takes the velocity to
  change.
• Acceleration (Final Velocity Initial
  Velocity)/Time
• a (vf vi)/t
• Unit of Acceleration meters per second per
  second (m/s/s or m/s2), miles per hour per second
  (mph/s), or kilometers per hour per second
  (km/hr/s).

18
Acceleration

• A decrease in velocity is called deceleration.
• Because the final velocity is less than the
  initial velocity, deceleration has a negative
  value.
• Deceleration is sometimes called negative
  acceleration.
• Example
• A roller coasters velocity at the top of a hill
  is 10-m/s. Two seconds later it reaches the
  bottom of the hill with a velocity of 26-m/s.
  What is the acceleration of the roller coaster?

19
Acceleration

• Examples
• A roller coaster has a velocity of 10-m/s at the
  top of a hill. Two seconds later it reaches the
  bottom of the hill with a velocity of 20-m/s.
  What is the acceleration of the roller coaster?
• A roller coaster is moving at 25-m/s at the
  bottom of a hill. Three seconds later it reaches
  the top of the next hill, moving at 10-m/s. What
  is the acceleration of the roller coaster?

20
Acceleration

• A change in velocity can be either a change in
  how fast something is moving or a change in the
  direction of movement.
• Any time a moving object changes direction, its
  velocity changes and it is accelerating.
• Examples
• A horse on a carousel. Although the speed is
  constant, the horse is accelerating because it is
  changing direction constantly as it travels in a
  circular path.
• The Earths orbit. The Earth is accelerating
  constantly as it orbits the Sun in a nearly
  circular path.

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Acceleration

• The data in the table to the right is of a
  professional drag-strip race.
• The driver traveled a distance of 5-m after 1-s.
• The distance covered in the next second was 15-m.
• By the end of 4-s, the driver had traveled 80-m.
• The graph is a curve rather than a straight line.
• A distance-time graph for acceleration is always
  a curve.

22
Acceleration

• Just as it was useful to graph a changing
  position versus time graph, it is also useful to
  plot an objects velocity versus time.
• Notice that the graph is a straight-line, which
  means that the object was speeding up at a
  constant rate.
• The rate at which the cars velocity is changing
  can be found by calculating the slope of the
  velocity-time graph.
• Slope Rise/Run
• The slope of the line is the acceleration of the
  object.
• Example
• What is the acceleration (slope) in this graph?
• a (20.0-m/s 10.0-m/s)/2.00-s
• a (10.0-m/s)/2.00-s
• a 5.00-m/s/s

23
Acceleration

• A speed-time or velocity-time graph can tell you
  whether the acceleration is positive or negative.
• If the acceleration is positive, the line slopes
  upward to the right.
• If the acceleration is negative, the line slopes
  downward to the right.

24
Motion and Forces

• A force is a push or a pull.
• A force may give energy to an object and cause it
  to start moving, stop moving, or change its
  motion.
• Ex Kicking a soccer ball at rest, hitting a
  tennis ball back to your opponent, playing
  billiards, etc.
• A force also may or may not produce a change in
  motion.
• Ex Two students pushing on a box against each
  other with equal amounts of force.

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Motion and Forces

• When two or more forces act on an object at the
  same time, the forces combine to form the net
  force.
• Forces on an object that are equal in size and
  opposite in direction are balanced forces.
• Ex Two students playing tug-of-war pulling with
  an equal amount of force but in opposite
  directions.
• Forces on an object that are not equal in size or
  opposite in direction are unbalanced forces.
• Ex Two students playing tug-of-war pulling with
  unequal amounts of force in opposite directions.

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Motion and Forces

• Adding forces
• If two or more forces are acting in the same
  direction, you can add them together to get the
  total or net force.
• Ex John and Sue are pushing a cart with a force
  of 5 lb. and 7 lb. respectively, in the same
  direction. Find the net force acting on the cart.

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Motion and Forces

• Subtracting forces
• If two or more forces act in opposite directions,
  you can subtract them to get the total or net
  force.
• Ex John is pushing to the right with 5 lb. of
  force on a cart. Sue is pushing to the left with
  7 lb. of force. Find the net force acting on the
  cart.

28
Motion and Forces

• Inertia is the tendency of an object to resist
  any change in its motion.
• Example
• If an object is moving, it will keep moving with
  the same speed and in the same direction unless
  an unbalanced force acts on it.
• The greater the mass of an object the greater the
  inertia.
• Mass is the amount of matter in an object.
• Example
• A bowling ball and a table-tennis ball are both
  moving at 5-m/s, which one is easier to stop?
  Why?
• The table-tennis ball is easier to stop because
  it has a small mass and therefore requires less
  force to stop its motion.

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Motion and Forces

• Forces change the motion of an object in specific
  ways.
• Sir Isaac Newton (1642 1727) was able to state
  rules that describe the effects of forces on the
  motion of object.
• These rules are known as Newtons Laws of Motion.
• These rules apply to the motion of all objects,
  no matter how large or how small.

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Motion and Forces

• Newtons First Law of Motion
• An object at rest remains at rest and an object
  moving with some velocity continues to move with
  the same velocity unless acted upon by an outside
  force.
• The tendency of an object to continue in its
  original state of motion is called inertia.
• Newtons first law is sometimes called the Law of
  Inertia.

31
Motion and Forces

• The law of inertia can explain what happens in a
  car crash.
• Example
• When a car traveling at 50-km/hr collides head-on
  with something solid, the car crumples, slows
  down, and stops within approximately 0.1-seconds.
• Any passenger not wearing a safety belt continues
  to move forward at the same speed the car was
  traveling.
• Within about 0.2-seconds, after the car stops,
  unbelted passengers slam into the dashboard,
  steering wheel, windshield, or the backs of the
  front seats.
• They are traveling at the cars original speed of
  50-km/hr.

32
Motion and Forces

• Safety belts loosen a little as its restrains the
  person, increasing the time it takes to slow the
  person down.
• This reduces the force exerted on the person.
• The safety belt also prevents the person from
  being thrown out of the car.
• Air bags, soft dashboards, crumple zones, etc.,
  all reduce injuries in car crashes by providing a
  cushion that reduces the force on the cars
  occupants.