2008-2010

:

1-

4 , ,

:

5-

20 .

5 11

:

21-

43 &

22 23 25 33 37

43-

47

44 45

48-

56 ,

57-

67 2

57 61

:

61-

89 ( )

69 70 73 75 78 80 81

1

1. ;

.

.. xA = +3m, x = -2m -

.

2. ;

,

.

x & x .

.. , -

:

x = x - x = (3 (-2))m = 5m.

, :

xA = xA - xA = (-2 3)m = -5m.

( ).

3. ;

() .

:

: m/s

-3 -2 -1 0 1 2 3 (m)

2

km/h.

, t = 2s,

:

:

:

, , , ,

(.., , , , ).

. ,

. , -

,

4. ;

s, -

. .

100m 50 .

s = 150m.

5. .

, , , ...

;

-

(s) (t) , :

3

s1 = 200m t1 = 100s.

t2 = 50s 400m t3 = 150s. :

S = (200+400)m = 600m

t = (100+50+150)s = 300s.

:

:

: :

.

. ( )

-

.

4

1. ,

-

x1 =

4m, x2 = 2m,

t1 = 4s. x3 = 6m.

t2 = 5s. , t3 = 10s x4 = -2m.

. .

. ;

. .

. ;

2. 10km 15min.

. ;

. t =10min

;

. ,

. ;

-5 -4 -3 -2 -1 1 2 3 4 5 6 7 8 9 10 (m)

5

1. .

( ). ,

.

x t .

(1)

x = x x, :

(2)

x () t

.

:

| | (3)

( ),

.

. = -10m/s.

x = 50m ( , . ). t =

40s:

x = t = -400m s = 400m.

x = x + t = -350m.

x x -

.

:

(1) (2) .

.

,

.

6

2.

- (x t) -

( x)

( t).

t, x,

.

( t = 0)

:

-

,

.

-

, x.

(0) , -

, .

( t = 0)

, ,

:

,

.

, -

.

-0.5 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 6.5 7 7.5 8 8.5 9 9.5

-0.5

0.5

1

1.5

2

2.5

3

3.5

t (s)

v (m/s)

1 2 3 4 5 6 7 8 9

2

4

6

8

10

12

14

16

18

20

22

24

26

28

t (s)

x (m)

x

x

t

t

7

5m/s,

. t = 0,

x = -10m, .,

:

x = -10 + 5t

, t1 = 2s,

t2 = 4s .

- .

x t ( ,

):

t = (3-1)s = 2s, :

= x = 10m

,

S = 10m.

2s 4s

0 10m

-0.5 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5

-14-12-10

-8-6-4-2

2468

1012141618

t (s)

x (m)

-0.5 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 6.5-0.5

0.51

1.52

2.53

3.54

4.55

5.56

6.57

7.58

8.59

9.5

t (s)

v (m/s)

8

1: . /.

9

1. x = 50m,

= 15m/s.

. t = 30s,

.

. ;

. =

-5m/s;

2. (x = 0)

to = 0 = 2m/s.

. t = 5s;

. 20m ,

;

. , , ;

3. 20

. t1 = 10s

1 = -2m/s. t2 = 5s 2 = 6m/s.

. 10s ;

. ;

. , (. .);

. ;

4. . 4m/s

x = -10m.

. t1 = 2s, t2 = 2,5s t3 = 5s.

. .

. .

10

. , .

5. , :

(t = 0) x = 0.

t1 = 5s x1 = 10m.

t2 = 7s. x3 =

4m, t3 = 10s

. (x-t) .

. tA(0 5s), t(5s 7s),

t(7s 10s);

. .

. ;

6.

- .

.

,

.

i)

; (

).

ii)

t = 0;

iii) ;

, :

. ( t )

.

. t = 4s.

0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5

2468

10121416182022242628

t (s)

x (m)

11

1. ( ;)

, .

. ,

( ) .

.. , -

= 2m/s -

= -

1m/s2.

-

. -

,

= -

4m/s =

-4m/s2 . -

( )

m/s2 ( S.I.)

2. - .

,

. (

), -

.

, -

, . -

.

(+)

12

,

:

(4)

,

t.

(4).

,

, (4) :

| | | | | |

, -

, (-)

, .

, , -

:

(5)

:

(6)

, (5 & 6) x, -

.

,

,

, :

| |

| | (7)

13

(-) .

.

, -

, :

; !

, , :

| | | | | | | | | |

| |

;

(7) ,

!

| |

| | | |

| |

| |

| | (

| |

| |)

, :

| |

.

1. 30m/s.

4m/s2. t = 2s, :

= | | ||t = (30-42)m/s =

22m/s

:

s =||t ||t2 =

= (302- 44)m = 52m.

:

| |

| |

:

| |

14

2. x =

2m, = 15m/s = -3m/s2.

-

,

:

= + t

= [15 +(-3)2+m/s

= 9m/s

:

x = x + t + t2 = *2+152 + (-3)4+m = 26m.

:

x = t + t2 = *152 + (-3)4+m = 24m.

, , -

:

s = | | t - ||t2 = *152 - 34+m = 24m

3. , x = 0

to = 0 = - 4m/s = 1m/s2.

t1 =

2s, -

:

1 = + t

1 = (-4 + 12)m/s

1 = -2m/s.

() 2m/s.

t2 = 4s, :

2 = (-4+14)m/s = 0, .

t3 = 6s:

3 = (-4+16)m/s = 2m/s. ,

2m/s. ( ).

-8 -6 0

15

:

x = x + t + t2.

:

x1 = (-42 + 14)m = -6m

x2 = (-44+ 116)m = -8m

x3 = (-46+ 136)m = -6m.

:

x = x3 x = (- 6 0)m = -6 m.

, :

x = t + t2

= (-46 + 162)m = -6m.

3. .

. ,

, .

, . , -

.

.. = 2m/s2 = 0, -

-

. ( 2s

4m/s).

, -

,

( )

( -

). ( 2).

2: . /

(m/s)

t(s) (m/s) t(s)

0 0 0 0 4 2 4 0 = 4 2-0 = 2 8 4 8 4 = 4 4-2 = 2

12 6 12 8 = 4 6-4 = 2 16 8 16 12 = 4 8-6 = 2 20 10 20 16 = 4 10-8 = 2 24 12 24 20 = 4 12-10 = 2

16

-

,

.

, -

.

:

-

,

. , , .

1 2 3 4 5

-4

-3

-2

-1

1

2

3

4

t (s)

(m/s^2)>0

17

1 2 3 4 5 6 7

5

10

15

20

25

30

35

40

45

50

55

60

65

70

75

t (s)

x (m)

: .

;

, .

().

, , -

(

)

18

1. = 2m/s2.

t = 0 x = 4m = 3m/s:

. ; ( ).

. t = 2s;

. ;

. ;

2. = -2m/s2.

t = 0 x = 0, = 4m/s:

. ; ( ).

. t = 1s;

. t;

. ;

3. = 2m/s2.

t = 0 = -5