ISBN 978-960-06-4826-3

: 0-22-0222

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. . .

. EM. .

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: , , , , , -, 2010, :I. , I. , . , . , . . .

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1.1

1. , :

st

=

120 m / s

4 = = 30m/s.

:

2. t, :

st+

=

st +=

1.980 20t s

10+

= t = 200s

3. A. To - :

1 2S E E= + S 10 10m 20 20m= + S 500m= .

. st

=

504

= 12,5m =

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8

.

4. .

(A): 1xt

= 1x t= (1)

(): 2s x

t

= 2s x t = (2)

(1) (2) :

1 2x s x t t+ = + ( )1 2s t= + 1 2

s 1.000t s10 15

= = + +

t 40s=

1

x :

1x t= x 10 40m= x 400m.=. :

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9

5. . t, - :

S t = S t = . :

( )S S t = d ( )t =

d 500t s

30 20 = =

t 50s=

. : S t 30 50m = = S 1.500m. =

6. x = 10t x = t , = 10m/s.

:

: s = t = 105m s = 50m, .

7. . 0 = 0 :

= t = 215m/s = 30m/s.. :

2 21 1s t 2 15 m2 2

= = s = 225m.

8. A. .

: 1s E 10 20m2

= = s = 100m.

. , ,

220 m / st 10

= =

22m / s . =

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10

s :

2 2 2 22 1 2 1

1 1 1 1s s s t t 2 2 m 2 1 m2 2 2 2

= = = s 3m= .

9. A. To .

: 30 10s 20m

2+

= s = 400m.

. : s 400 m / st 30

= = 40 m / s.3

=

10. = 8 + 2t = 0

+ t,

0 = 8m/s = 2m/s2.

:2 2

4 2 0 4 4 0 2 21 1s s s t t t t2 2

= = +

( ) ( )2 20 4 2 4 21s t t t t2= + ( ) ( )1s 8 4 2 2 16 4 m2

= +

s = 28m

11.

A. - = f(t) . - t = 6s = 30m/s.

. () 10s .

: 11s 10 50m2

= s1 = 250m.

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11

() 10s . : s

2=1030m s

2= 300m.

() () t = 10s s = 300m 250m s = 50m.

. t . , :

( )t t 1050 30t

2+

= 10t 50 = 6t t = 12,5s.

12. -

.

:t = + 30 10= + ()

21t t2

= + 1200 10 1002

= + ()

() ()

.

() : = 30 10 ()

() :200 = (30 10)10 + 50 = 2m/s2.

() : ( )30 10 2 m / s = A 10m / s. =

13. 0,7s 0

, 1 0 1s t 20 0,7m= = 1s 14m.= s = (50 14)m s = 36m.

:2 2

0max

20s m2 2 10

= =

maxs 20m.=

smax

< s .

14. ( )s m.+ - = 2m/s2,

0 = 20m/s.

: ( ) 201s t t2

+ = + 2170 55 20t 2t .2

+ = +

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12

t1 = 25s

t2 = 5s .

15. . . : 1 2x x=

210t 4t= 4t 10= t 2,5s.=. -

1=10m/s,

0 = 0 = 8m/s2.

:

16. . 11s

1 9 6S 3 9 5 9 3 m2 2

+ = + +

S 81m. =

:

S 81m / st 11 = = 7,36m / s. =

. 3s

21

9 0 m / st 3

= =

21 3m / s = , 3s -

223 m / s

t 3

= =

22 1m / s . =

17. . :

0 t = 0

0 t2

= 5 = 10 2t t = 2,5s

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13

201s t t2

= 21s 10 2,5 2 2,5 m2

=

s 18,75m.=

. 0 t = = 0

: 00 t= 0 10t s

2

= =

t 5s.=

() :2 2

0max

10s m2 2 2

= =

maxs 25m.=

18. . ts, - (t 4)s . :

2

11s t2

= ( )221s t 4 .2

=

s s = , :

( )221 21 1t t 42 2 = ( )2 21,6t 2,5 t 16 8t= +

t = 20s 4 s

1,8

4s.

21s s s 1,6 20 m2

= = =

s = 320m.

. :

=

1t = l,620m/s

=32m/s

=

2(t 4) = 2,5(20 4)m/s

= 40m/s.

16m / s. = : s 320 m / st 20

= = 16m / s. =

. = f(t) s = f(t) :

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14

19. . : 0 t 5s

0= 10m/s.

: 5s < t 15s

= 20m/s. : 15s < t 20s -

21 4m / st

= =

.

-

22 4m / s .t

= =

. 0 t 5s :

2 21

1 A

20 10 m / s 2m / st t t 5 0

= = = =

.

. .

( )10 20 1 1s 5 10 20 20 5 5 20 m 75 200 50 50 m 375m2 2 2+ = + + + = + + + =

:x = (75 + 200 + 50 50)m x = 25m. .

. : s 375 m / st 25

= = 15m / s. =

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1.2

1. :

( )1 2F F F 80 60= + = + F 140N= .

: ( )1 2F F F 80 60= = F 20 .=

2. F :

F = (20 + 10) 5 F = 25N F = 20 (10 + 5) F = 5 F = (20 + 10 + 5) F = 35

3. . -

1 2F F F .= +

2 2F 4F F= + 2F 2= 1 2F 4F= 1F 8N.= - .

. -

1 2F F F .= 2 2F 3F F= 2F 5N= 1 2F 3F= 1F 15= . .

4. . Hooke : F = Kx. x = 20cm F = 80N :

80 = 20cm 80 NK20 cm

= K Ncm

= 4 .

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16

, = x - :

(cm) 5 8 10 15 20

() 20 32 40 60 80

. :

. -

: 20N 4N / cm5cm

= = =

,

.

5. , = 0, - F = m, F = 0. - F

3

F2, :

1 2 3F F F 0 = ( )3 1 2F F F 22 7 N= = 3F 15N.=

6. , - F, F . : F B = 0 F = B F = 200 .

7. F F = 20N , . , - .

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17

8. t

=

:

2 25 m / s 2,5m / s2

= = .

: F = m = 102,5N F = 25.

9. = 4t = t = 4m/s2. :

F = m = 14 F = 4.

10. :

214 10 m / st 2

= =

22m / s . =

: F = m = 102N F = 20N.

11. . :

211

1

F 4 m / sm 1

= = 21 4m / s =

222

2

F 15 m / sm 3

= = 22 5m / s . =

. 18m t S

1 S

2 :

( )2 1S S 18 10 m = 2 1S S 8m = . :2 2

2 11 1t t 82 2 = 2 2

1 15t 4t 82 2

=

2 22,5t 2t 8 = 2t 16= t 4s.=

12. . 211F 20 m / sm 20

= =

21 1m / s = t1, 0

s1. :

21 1 1

1s t2

= 21 11s t2

= ()

0 1 1t = 0 1t = ()

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18

222

F 5 m / sm 20

= = 22 0, 25m / s =

0 12

2 2

tt

= =

()

2 2

0 12

2 2

ts

2 2

= =

()

1 2s s s+ = 2

2 11

2

t1 t s2 2

+ =

2 21 1

1 t 2t 402

+ = 1t 4s.=

F2

2 21 1

1 1s t 4 s2 2

= = 1s 8m.=

. :

11 2 1

2

t 4t t t t 4 s0,25

= + = + = +

t 20s. =

13. . :

21s t2

= 222s 48 m / s

16t = = 23m / s . =

. F m= 1 2 3F F F F = + -: F F F m1 2 3+ = 36 2 F 1 3+ = 3F 5N.=

14. 1 2F F F 40 20 = = F 20 . =

F = m m = 200,3

kg.

:

F m = 2F 40 m / s20m0,3

= = 20,6m / s . =

, - .

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19

15. :

21h gt2

= 22htg

= 2htg

=

t = 2s.

16. t, :

21h gt2

= 2htg

= t = 6s.

t :

t = t t t = (6 l)s = 5s.

2 21 1h gt 10 5 m2 2

= = h = 125m.

h :h = h h = (180 125)m h = 55m.

17. A. :

F = m 4

2 2F 2 10 m / s 5m / s .m 4.000

= = =

:2

0s2

=

20 2 s = 0 2 s =

0 = 20m/s.

. :

0 20t s5

= =

t s = 4 .

. :

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20

18. . t. :

21h gt2

= 2htg