Projectile Motion Projectile motion is motion that

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Projectile Motion Projectile motion is motion that Powered By Docstoc
					Accelerated Motion
           Changing motion
• You can feel the difference between
  uniform and nonuniform motion
• When motion changes, you feel a push or
  pull (a force).
  – Ex: a Marta train coming to a sudden stop
• In uniform motion, your body becomes
  used to it.
  – Ex: sitting in a car on cruise control
              Acceleration
• Whenever we change our state of motion,
  we are accelerating.
• Acceleration is how quickly we are
  changing our velocity
• Acceleration: the rate at which
 velocity is changing
  – SI unit: m/s2 or meters per second per
    second
  – Ex: speeding up, slowing down (negative
    acceleration), changing direction
  Check Your Understanding
If a dog chases its tail in a circle at the
   same speed the whole time, is it
   accelerating?
Yes! Even though its speed is staying
 constant, it is changing direction, and
 therefore changing its velocity. If the
 velocity changes, it is accelerating.
– Equation:   a = Δv / t = (vf – vi) / t
  • a = acceleration (m/s2)
  • Δv = change in velocity (m/s)
  • vf = final velocity (m/s)
  • vi = initial velocity (m/s)
  • t = time (s)
    Check Your Understanding
Suppose a car moving in a straight line
  steadily increases its speed each
  second, first from 35 to 40 km/h, then
  from 40 to 45 km/h, then from 45 to 50
  km/h. What is its acceleration?

 We see that the speed increases by 5
  km/h each second. The acceleration
  would be 5 km/h.s during each interval.
  Check Your Understanding
In 5 seconds a car moving in a straight line
  increases its speed from 50 km/h to 65
  km/h, while a truck goes from rest to 15
  km/h in a straight line. What is the
  acceleration of each vehicle?
                   a = Δv / t
acar = ?                  atruck = ?
Δvcar=65–50=15 km/h       Δvtruck=15-0=15 km/h
t = 5s                             t = 5s
acar = (15 km/h) / (5s)   atruck = (15 km/h) / (5s)
acar = 3 km/h.s           atruck = 3 km/h.s
  Check Your Understanding
Which undergoes a greater acceleration?

Although the speeds are different, their
 rate of change of speed is the same…so
 both have the same acceleration.
              Elapsed Time
Elapsed time: the time that has passed
 since the beginning of a fall
  – How long it takes something to fall
  – SI unit: seconds
                    Free Fall
• Consider an apple falling from a tree. We
  know that it starts at rest and gains speed
  as it falls, or accelerates.
• Gravity causes the apple to accelerate
  downward and is said to be in free fall.
Free fall: when an object is only
  affected by gravity
  – SI unit: m/s2 ( for acceleration due to gravity)
  – Ex: g = 10 m/s2 on Earth.
     • The letter g represents the acceleration due to
      gravity.
  – Equation:   v = gt
     • v = velocity or speed (m/s)
     • g = acceleration due to gravity (10 m/s2 on
       Earth)
     • t = elapsed time (s)

**Hint - as soon as you see any of the
  following phrases in a word problem, write
  g = 10 m/s2 for a given: free fall, falling,
  dropped, thrown**
   Check Your Understanding
What would the speedometer reading on
 a falling rock be 4.5 seconds after it
 drops from rest?

                 v = ?
               g = 10 m/s2
                 t = 4.5s
                 v = gt
           v = (10 m/s2) (4.5s)
              v = 45 m/s
How about 8 seconds?
                   v=?
                 g = 10 m/s2
                    t = 8s
                    v = gt
              v = (10 m/s2) (8s)
                 v = 80 m/s

How about 15 seconds?
                   v=?
                 g = 10 m/s2
                   t = 15s
                    v = gt
              v = (10 m/s2) (15s)
                v = 150 m/s
• Now consider an object thrown straight up.
  It will continue to move straight up, then it
  comes back down.
• At the highest point, the object changes its
  direction and the objects instantaneous
  speed is 0 m/s.
• Whether the object is moving up or down,
  the acceleration of the object is always 10
  m/s2.
• Because an object in free fall increases
  the rate of distance covered every second,
  we cannot use v =d/t.
  – Equation: d = ½ gt2
     • d = distance (m)
     • g = acceleration due to gravity (10 m/s2 on
       Earth)
     • t = elapsed time (s)
    Check Your Understanding
What is the distance an object falls in one
 second?
                 d = ?
                 g = 10 m/s2
                    t=1s
                  d = ½ gt2
                d = ½ (10)(12)
                   d=5m
     Air Resistance and Free Fall
• All objects fall at 10 m/s2 on Earth
   • Regardless of weight or mass
   • Ex: In a vacuum, a feather and a bowling ball will hit
     the ground at the same time if dropped from the same
     hieght
      • A vacuum is anyway without any air (ex: outer space)
• Air resistance causes objects such as a coin and
  a feather to accelerate differently.
   • However, air resistance less noticeably affects the
     motion of more massive objects like stones and
     baseballs.
• With negligible air resistance, falling objects can
  be considered to be in free fall.
        Velocity – Time Graphs
• Velocity-Time graphs
                             60
  show the change of
  velocity over an           50

  elapsed time               40
  – AKA Speed-Time
                             30
    graphs
     • Remember that speed   20
       does NOT take into
       account direction     10

• Time is always the         0
                                  0   10   20   30   40   50
  independent variable
• Velocity is always the
  dependent variable
• The slope of a Velocity-Time graph is equal to
  acceleration
• Slope = rise/run
• Slope = change in velocity / time
  – a = Δv / t
  – The steeper the slope, the faster the acceleration
     • Remember acceleration can be speeding up, slowing down,
       or sharp turns
  – A positive slope is speeding up and moving forward
  – A negative slope is EITHER slowing down OR moving
    backwards
  – A zero slope means that the velocity is NOT
    changing, meaning that the object is moving at the
    same speed in the same direction
Check Your Understanding
            Which person(s) could
             be slowing down?
             Person C. They have
              a negative slope; they
              could be moving
              backwards too (there
              is not enough info on
              the graph to tell).
Check Your Understanding
            Which person(s) are
             not accelerating?
             A and E. Their have
              a constant velocity.

            Which person(s) could
             be speeding up?
             B and D. They are
              increasing velocity
              each second.