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					Speed, Velocity and Acceleration

          Linear Motion
              Linear Motion
• The following quantities are used to describe
  motion: speed, velocity and acceleration
• Each of these is a rate. A rate is a quantity
  divided by time.
• Motion along a straight line is sometimes
  called linear motion.
         All Motion is relative
• All motion is relative to a reference.
• In our environment, the reference for motion
  is the earth’s surface, and speeds are
  measured relative to the earth
• The earth moves at 107,000 km/h relative to
  the sun
 • Speed is a measure of how fast something is
 • Units of speed could be: km/h, m/s, mi/h, ft/s
 • In physics we use units of m/s for speed

 •                                 s = d/t
speed                    d

                      s       t
         Instantaneous Speed
• Instantaneous speed is speed at any instant in
• A speedometer measures speed in ‘real time’
  (the instantaneous speed).
             Average Speed
• Average speed is the average of all
  instantaneous speeds; found simply by a total
  distance/total time ratio
• The average speed of a trip:
                         total distance
       average speed 
                          elapsed time
                  Velocity vs. Speed
• Speed refers to how quickly an object moves
• Velocity is defined as speed in a given direction or rate of
  change of position (displacement over time). v = x/t
• Velocity refers to both the speed and direction
• Negative velocity means the object is moving in the opposite
• Motion at constant velocity means that both the speed and
  direction of an object do not change.
• In a car, we can change the velocity three ways: gas pedal to
  speed up, brake to slow down or steering wheel to change
            Velocity Triangle
• Speed and velocity triangles are similar
  because v = x/t
• Find the equation for displacement, and time
  using the triangle
• x=vxt
• t = x/v               x

                    v    t
             Velocity Questions
1) How far does Bob run if he maintains an average
   velocity of 3 m/s for 10 s?
2) List three ways you can change the velocity of your
3) Is it possible to go around a corner without
   changing velocity? Explain.
4) One car is going 25 miles/hr north, another car is
   going 25 miles/hr south. Do they have the same
   velocity? Explain.
1.       What is the speed of a truck
 that travels 10. km in 10. minutes?
2.       What distance is traveled by
a police car that moves at a constant
   speed of 1.5 km/minute for 5.0
  3.     What distance would be
 covered in 10. minutes by a train
that travels at a constant speed of
  500. meters every 10. seconds?
 4.     What is the average speed
of a commercial jet that travels from
 New York to Los Angeles (4800 km)
           in 6.00 hours?
  6.     A car is traveling at an
 average speed of 70. m/s. How
many km would the car travel in 6.5
The pilot of a light plane heads due
     North at an airspeed of 180
    km/h. A wind is blowing from
    the West at 60. km/h. What is
   the plane’s velocity with respect
             to the ground?
A car moved 60 meters West in 2
      hours. What is its average
A moon rock is for the rock to fall 6.6
   meters dropped from a cliff and
    it takes 2 seconds. What is the
      moon rock’s average speed?
   A car travels 1000 meters in 5
seconds. What its average velocity?
A boy walks 500 meters in 10
  seconds. What is his average
Jane rolled a ball 600 meters. What
      was her average velocity if it
          took her 10 seconds?
What is the average velocity of a dog
   that runs 7500 meters that in 10
What is the average velocity of a car
   that coasts 3000 meters in 300
How far will a horse trot at a velocity
        of 4 m/s for 1 minute?
What is the average velocity of a
  student who walks 800 meters
           in 78 seconds?
What is average velocity of a dog
   who walks 100 meters in 20
An object travels at a velocity of
  18.99 m/s for a time period of
    15.63 seconds. What is its
An object travels at a velocity for a
    time period of 12.19 seconds
    over a displacement of 10.56
   meters. What is the value of this
          constant velocity?
An object travels at a constant
  velocity of 14.23 m/s for a time
 period of 11.19 seconds. What is
 its displacement over this time?
An object travels at an average
     velocity of 15 m/s for 23
       seconds. What is its
  displacement over this time?
How long will a dog run at a pace
     of 2 m/s over 12 meters?
• For its velocity to change, an object must
• An object accelerates whenever its speed or
  direction or both change.
• Acceleration may be positive (increasing speed)
  or negative (decreasing speed).
• Acceleration is a measure of how quickly the
  velocity changes: a = Dv/t
                     change of velocity
      acceleration 
                        time interval
   Acceleration at constant speed
• An object moving in a circle at constant
  speed is always accelerating (changing
  Solving Acceleration Problems using
          Acceleration Triangle
• If not, use triangle to find change in velocity (Dv),
  then find initial or final velocity
• Dv = ending velocity – starting velocity
• Acceleration = Velocity Final – Velocity Initial
             »               Time


                                             a        t
A dragster going at 15 m/s increases its
      velocity to 25 m/s in 4 seconds.
         What is its acceleration?
 The driver of a car steps on the brakes,
and the velocity drops from 20 m/s to 10
  m/s in a time of 2 seconds. Find his
Find the acceleration of a car that travels
      at a constant velocity of 45 Km/hr
                   for 10 s.
Challenge: Calculate the velocity of a
  skateboarder who accelerates from
   rest for 3 seconds down a ramp at
        an acceleration of 5 m/s2.
A roller coaster car rapidly picks up
speed as it rolls down a slope. As it
starts down the slope, its speed is 4
  m/s. But 3 seconds later, at the
bottom of the slope, its speed is 22
      m/s. What is its average
. A cyclist accelerates from 0 m/s to
   8 m/s in 3 seconds. What is his
         acceleration ? Is this
  acceleration higher than that of a
 car which accelerates from 0 to 30
          m/s in 8 seconds?
  A car advertisement states that a
certain car can accelerate from rest
 to 70 km/h in 7 seconds. Find the
     car’s average acceleration.
4. A lizard accelerates from 2 m/s to
  10 m/s in 4 seconds. What is the
    lizard’s average acceleration?
5. If a Ferrari, with an initial velocity
of 10 m/s, accelerates at a rate of 50
  m/s/s for 3 seconds, what will its
           final velocity be?
   A skater increases her velocity
from 2.0 m/s to 10.0 m/s in 3.0
 seconds. What is the skater’s
  A car accelerates at a rate of 3.0
m/s2. If its original speed is 8.0 m/s,
 how many seconds will it take the
 car to reach a final speed of 25.0
 While traveling along a highway a
driver slows from 24 m/s to 15 m/s
     in 12 seconds. What is the
     automobile’s acceleration?
 (Remember that a negative value
    indicates a slowing down or
  A parachute on a racing dragster
opens and changes the speed of the
   car from 85 m/s to 45 m/s in a
 period of 4.5 seconds. What is the
    acceleration of the dragster?
 A car traveling at a speed of 30.0
m/s encounters an emergency and
 comes to a complete stop. How
much time will it take for the car to
stop if it decelerates at -4.0 m/s2?
 If a car can go from 0 to 60 mi/hr in
 8.0 seconds, what would be its final
speed after 5.0 seconds if its starting
         speed were 50 mi/hr?
A cart rolling down an incline for 5.0
 seconds has an acceleration of 4.0
  m/s2. If the cart has a beginning
  speed of 2.0 m/s, what is its final
A helicopter’s speed increases from
25 m/s to 60 m/s in 5 seconds. What
     is the acceleration of this
  As she climbs a hill, a cyclist slows
down from 25 mi/hr to 6 mi/hr in 10
 seconds. What is her deceleration?
  A motorcycle traveling at 25 m/s
accelerates at a rate of 7.0 m/s2 for
6.0 seconds. What is the final speed
        of the motorcycle?
A car starting from rest accelerates
 at a rate of 8.0 m/s/s. What is its
   final speed at the end of 4.0
 After traveling for 6.0 seconds, a
runner reaches a speed of 10 m/s.
What is the runner’s acceleration?
        Free fall, an example of
• Free fall is when an object is falling being
  affected only by gravity. That means NO air
Free Fall – All objects fall at the same rate

           • If you drop a coin and a feather at the
             same time you will notice that the coin
             reaches the ground way before the
           • However, if you were to take the air
             out of the container you would find
             that the coin and feather fall together
             and hit the bottom at the same time!
      Acceleration due to gravity, g
• Newton told us that every object with mass attracts every
  other object with mass and the size of the attraction depends
  on the mass of each object and the distance between the
• We don’t feel the attraction of most objects because their
  mass is small relative to the Earth which has a huge mass.
• The Earth pulls so that objects experience an acceleration of
  about 9.8 m/s2. This acceleration is given a special letter, g.
• g = 9.8 m/s2 This number is important, remember it!
• So during each second an object is in free fall, its velocity
  increases by 10 m/s. If the object experiences air resistance its
  velocity won’t increase as fast because air resistance will slow
  it down.
            Challenge Question
• Suppose someone throws a ball
  straight upward with a speed of 30
  m/s and at the same time throws one
  straight down with a speed of 30 m/s.
  Which ball will be traveling faster
  when it hits the ground, the one
  thrown straight upward or the one
  thrown straight down? Assume there
  is no air resistance.
Time and velocity for an object in free fall
                          v = gt


g       t
Time and Distance for an object in free fall
                         d = ½ gt2

        Free Fall Questions – How Fast?
1) When a ball is thrown straight down, by how much does speed increase
    each second on Earth?
2) When a ball is thrown straight up, by how much does speed decrease each
3) In free fall, do a feather and a ball fall side by side? Explain.
4) An apple falls freely from rest for 8 s on Earth, find its speed at 8 s.
5) Suppose a rock is dropped on a planet where the acceleration due to
    gravity it 5 m/s2, by how much would the speed change each second?
6) If a rocket on the planet in #5 falls from rest for 3 s, what is its speed at the
    end of the 3 s interval?
7) Challenge: Find g on a planet where a rock has a velocity of 120 m/s after
    6s of free fall.
           Free Fall Questions – How Far?
1)   For a freely falling rock does the distance fallen each second stay the
     same, increase with time, or decrease with time?
2) A ball is dropped from rest and freely falls for 6 s. How many meters has
     it fallen in 6 s?
3) A ball is thrown straight upward and travels 5 m until it reaches the top
     of its path.
    a) How far will it fall before it reaches its initial position?
    b) How long will it take to fall that distance?
    c) How long will the ball be in the air?
4) A ball is thrown straight up and returns to Earth 6 s later.
    a) Find its speed at the top of its path.
    b) Find its acceleration at the top its path.
    c) How long does it take to reach the top of its path?
    d) How fast is it traveling when it returns to Earth?
    e) Challenge: What is its maximum height?
    Additional Free Fall Review
1) If one had only a stopwatch, could one
   determine the initial speed of a ball
   launched vertically upward from the earth’s
   surface? Explain.

2) With only a stopwatch, could one
   determine how high the ball travels before
   it stops? Explain.
        Motion Graphs – Position vs. Time

constant, rightward (+) velocity of +10 m/s

        a rightward (+), changing velocity - that is, a car that is moving
        rightward but speeding up or accelerating
         Motion Graphs – Velocity vs. Time

constant, rightward (+) velocity of +10 m/s

         a rightward (+), changing velocity - that is, a car that is moving
         rightward but speeding up or accelerating
         Motion Graph Questions
1) What do you think might be happening in this graph?

                2) What do you think position
                   and velocity graphs of free
                   fall motion might look like?
                   Try to sketch them.

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