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Grade 8 speed and acceleration

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					Chapter 12 What is motion?
Describing Motion




Point of reference: An object or group of
objects that is considered to be stationary
Point of Reference




 From the man standing outside’s perspective, what is
 happening to the bus?
 From the bus driver’s perspective, what is happening to
 the man?
  Point of Reference




From this driver’s perspective, is he standing still, moving
forward or backwards?
What about the car in his rear view mirror?
The buildings in front of him?
12.1 Measuring Motion

n   Distance – the total length that an object has
    travelled.

n   Displacement – the distance and direction from
    the starting point to the ending point. Path taken
    is not important.
12.1 Measuring Motion


                                Displacement

        distance

                        displacement
12.1 Measuring Motion



How do we accurately
communicate distance
and displacement?
    12.1 Measuring Motion


n   A scalar is a quantity that
    can be completely
    described by one value:
    the magnitude (size).
    12.1 Measuring Motion

n    A vector has both
     distance and direction.

n    If you walk five meters
     east, your displacement
     can be represented by a
     5 cm arrow pointing to
     the east.
12.1 Measuring Motion

  Both Mr. Rabbit and Mr. Tortoise took the
  same round trip, but Mr. Rabbit slept &
  returned later.
   12.1 Measuring Motion
   Who runs faster?
                           No, I travelled
 Me, as I spent         longer distance every
less time on the               minute.
       trip.




      Comment on their argument.
Speed
How can we describe how fast an object moves?

E.g. A car on Jal el Dib Highway travels
    90 km in 1 hour.

   We say that the car travels at a speed
   of 90 km/h.
Speed
How can we describe how fast an object
moves?
Speed is a measure of how fast something
moves.

Speed = distance travelled per unit of time
 SI unit: m/s or km/h (for long distances)
Speed
                                     Distance vs Time
                                Distance vs.Time
               12



               10


                                                        B
Distance (m)




                8



                6



                4


                        A
                2



                0
                    0       1         2           3         4   5


                                     Time (s)
Speed
Average speed

 Average speed does not tell the
 variations during the journey.

   On most trips, the speed at any
   instant is often different from the
   average speed.
Speed
   Average speed
 A car travels at 50 km/h, for an hour
    slows down to 0 km/h, for an hour
and speeds up to 60 km/h for another hour.

 Its average speed over the whole journey
              50 distance km
          overall km + 60 travelled
       =
             total time of travel
                    3h
              = 36.7 km/h
Average Speed
Calculate the average speed of the car at point A
and point B
                                              Distance vs. Time
                 35

                 30                                                        B
                 25
  Distance (m)




                 20

                 15

                 10
                              A
                 5

                 0
                      0   1       2   3   4    5   6   7   8   9 10 11 12 13 14 15 16
                                                       Time (s)
                            Distance vs. Time
              140

              120

              100
Distance(m)




               80

               60

               40

               20

                0
                    0   1       2         3     4   5

                               Time (s)
Speed
  Instantaneous speed
 Instantaneous speed = speed at any instant

The word ‘speed’ alone  instantaneous
                         speed
Instantaneous speed
 distance travelled in an extremely short
time interval
Speed
  Instantaneous speed




  Speedometer tells the car’s speed
          at any instant!
Q1 The world record...
The world record of women 100-m race
is 10.49 s.
What is the average speed?
                      ( 100 m )
Average speed =
                       10.49 s

             = 9.53 m/s or 34.3 km/h
  (9.53 m/s x 3600 s/h = 34308 m/h
                       = 34.3 km/h )
Q2
A man walks from A to B at 1 km/h
           and returns at 2 km/h.

  A             1 km/h
                                   B

                 2 km/h

     Average speed for the whole trip = ?
Q2

     A         1 km / h
                                  B

                2 km / h

Suppose AB = 1 km  whole journey = 2 km
                       1 km   1 km
Time for whole trip =       
                      1 km/h 2 km/h
                  = 1 h + 0.5 h = 1.5 h
Avg. speed = distance / time = 1.33 km/h
                             = 2/1.5
12.2 Velocity
Velocity is...
  rate of change of displacement or
    a speed in a given direction.

                 direction
velocity                       a vector
                               quantity
                 magnitude
                  (speed)
 Velocity
     Speed with direction
                         A subway driver’s
                         concern is speed only.
speed = 90 km h–1



 A pilot’s concern is
 velocity (direction &
 speed).                  speed = 300 km/h
                          direction = west
Velocity
         Average velocity
                        overall distance
Average velocity =
                      total time of travel



                        direction of overall
Direction of velocity =
                        distance
Velocity
    Instantaneous velocity
The velocity at any instant is called
instantaneous velocity.

If a car moves at a constant velocity...
… its average and instantaneous velocities
have the same value.
So Who is Faster?




                                  Rabbit –
                          instantaneous velocity
               Answer? They
 Tortoise – average
  velocity over the        at the beginning and
                  BOTH are! end of the race
     whole race
 Q1 In an orienteering event...
In an orienteering event, Maria and Karen
reach their control points at the same
time.
                        start, 10:00 am
Maria, 10:30 am



                             Karen, 10:30 am

 Who runs at a higher average velocity?
    Q1 In an orienteering event...

    Who runs at a higher average velocity?

A     Maria.
B     Karen.
C     Undetermined since their paths are
      unknown.
D     Incomparable since they run along
      different directions.
Example 1
A car travels from Batroun to the airport in
Beirut. Use the formula, s=d/t to calculate
a, b and c in the following table:

                   Batroun  Jounieh    Antelias
                   Jounieh Antelias    Airport
Distance between     30       15.4          (a)
cities/ km
Travel time btw      17        (b)          16
cities/ min
Avg. speed btw       (c)       90           55
cities/ km/h
 Example 1
(a) Antelias  Airport:
  Distance = avg. speed  time
           = 55 km/h  0.267 h = 14.7 km
                   Batroun  Jounieh    Antelias 
                   Jounieh Antelias    Airport
 Distance between     30      15.4          (a)
 cities/ km     = (16min/60min/h)
                =      h
 Travel time btw 0.26717       (b)          16
 cities/ min
 Avg. speed btw      (c)       90           55
 cities/ km/h
 Example 1
(b) Jounieh  Antelias:
 Time = distance / avg. speed
      = 15.4km/90km/h = 0.171 h =10.3min
                       Batroun  Jounieh    Antelias 
                       Jounieh Antelias    Airport
 Distance between         30      15.4        (14.7)
 stations / km
 Travel time btw
 Journey time             17       (b)          16
 between min
 stations /stations / s
 Avg. speed btw
 Ave.        between      (c)      90           55
 stations / km/h–1
            km h
 Example 1
(c)     Batroun  Jounieh:
      Avg. speed = distance / time
                 = 30km/ 0.283h = 106 km/h
                         Batroun  Jounieh    Antelias 
                         Jounieh Antelias    Airport
      Distance between    30.0      15.4        (14.7)
      stations / km
      Time between         17      (10.3)     16
      stations / min                =
                                    (17min/60min/h)
      Ave. speed btw       (c)      =90
                                      0.283 h 55
      stations / km/h
Example 1
(d) What was the total average speed for the
whole trip?
              Total distance
              (30+15.4+14.7)km
 Avg. speed =
   60.1km
             (17+10.3+16)min/60min/h
                Total time
 = 83.3 km/h
   0.722h          Batroun  Jounieh    Antelias
                   Jounieh Antelias    Airport
Distance between     30       15.4        (14.7)
cities/ km
Travel time btw      17      (10.3)         16
cities/ min
Avg. speed btw      (106)      90           55
cities/ km/h
Acceleration

When a car moves
faster and faster,
its speed is increasing
(velocity changed).
Acceleration

When a car moves
slower and slower,
its speed is decreasing
(velocity changed).
Acceleration

When a car changes
direction, its velocity
changes too.
 Acceleration
Acceleration measures the change in velocity

                 direction        speed
 Acceleration = velocity per unit time

                overall change in velocity
              =
                     total time taken

 Unit: m s–1 / s = m s–2     vector quantity
      Acceleration
  If a car accelerates at 2 m/s2, what does that mean?


t=0         v=0
             t = 1 s v = 2 m/s,
                     v = 2 m/s
      2m
                        t = 2 s v = 4 m/s,
                                v = 2 m/s
           4m
                                              t=3s
                                              v = 6 m/s,
                           6m
                                              v = 2 m/s
Acceleration
The Ferrari 348 can
go from rest to
100 km/h in 5.6 s.
What is its avg. acceleration (in m/s2)?
Avg. acceleration                   1km/h =
                                1km/h = 1m/3.6s
                                  1000m/3600s
  100 km/h          (100/3.6) m/s
=               =
     5.6 s              5.6 s
= 4.96 m/s2
Speed Graph
 Acceleration Graph

      25m/s




                          45s          90s   110s



What is:
a) The acceleration between O and A?
b) The acceleration between A and B?
c) The acceleration between B and C?
Q1 A running student...

A running student        +ve
is slowing down in
front of a teacher.
With reference to the
sign convention,


Velocity of student:     positive / negative
Acceleration of student: positive / negative
Q2 In 2.5 s, a car speeds up...

In 2.5 s, a car speeds up from 60 km/h to
65 km/h...
…while in 2.5 s, a bicycle goes from rest to
5 km/h.


Which one has the greater acceleration?

   They have the same acceleration!
Q3 A car is moving in a positive direction...

  A car is moving in a +ve direction.
  What happens if it moves under a ve
  acceleration?
            The car will slow down.
  What happens if it moves under a ve
  deceleration?
      The car will move in +ve direction
      with increasing speed.
 Note
Unit of time: hour (h)
                         (or s if using small numbers)

Unit of distance: kilometer (km)
                                  (or m if using small numbers)


Quantity            Unit            Scalar/Vector
Speed              km/h
                   ______                     scalar
                                              _____
Velocity           km/h
                   ______                     vector
                                              _____
Change in velocity ______
                   km/h                       _____
                                              vector
Acceleration       km/h2
                   ______                     vector
                                              _____
The End
                            Distance vs. Time
              140

              120

              100
Distance(m)




               80

               60

               40

               20

                0
                    0   1       2         3     4   5

                               Time (s)
 Example 1
Airport Express takes 0.35 h to go from
Batroun to the Airport (34 km).
 Avg. speed = 34 km/0.35 h = 97 km/h
                      Batroun  Jounieh      Beirut dis.
Complete the table.   Jounieh Beirut dis.   Airport
 Distance between       2.6        8.9           (a)
 stations / km
 Travel time btw        153        (b)           762
 stations / s
 Avg. speed btw         (c)         90           105
 stations / km/h

				
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