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www.methodiko.net & 2, , : 210 99 40 999 . 201, , : 210 96 36 300
:
( 2, 4) .
.
.
1. H, - .
) . (K) (y) , :
) ) )
4 ) .
8
2. m - F, = 2g, g -.
) :
) F ) 3F ) F3
4
) .
9
F
K
0 y
()
0
K
H y
()
K
0 yH
()
Iro Markaki 1
mA = 5 kg mB = 10 kg, x. t = 0 s xo = 0 m, . = 10 m/s, = 30 m/s, -
= 2 m/s2 .
:
1) , 5
2) t,
6 3) ,
8 4) to = 0 s, .
6
www.methodiko.net & 2, , : 210 99 40 999 . 201, , : 210 96 36 300
1
- :
1.
: )
. 2.
: )
: = = = 2 = 2 =
- :
1. ... : = 0. : = = 20 / 2. : = = 10 = 30
2 0 = 20 0 = t(20 t) = 20 .
3. : = = 30 2 = 10 = 10. 4. : = 0 . : =
= 5 10 5 30 = 500 4500 = 4000.
1. m . h .
) .
:
) mgh ) 0 ) 2mgh 4
) .
8
2. .
.
) .
0 s - 30 s :
) +300 m ) +600 m ) 300 m 4
B) . 9
Iro Markaki 2
m = 2 kg = 0,5. t = 0 s, F
& 30 N t = 3 s, -
F&. g = 10 m/s2.
.
:
1) , 6
2) F , 6
3) , 6
4) t = 0 s .
7
m F
www.methodiko.net & 2, , : 210 99 40 999 . 201, , : 210 96 36 300
2
- :
1.
: ) 0
, . 2.
: )
: 0 10 : = = 30 10 = 300 . : 10 20 , . 20 30 , ( ) . , : + = = 300 .
- :
1) : = = 0,5 = 0,5 2 10 = 10 2) : = = 20 = 2 = 10 / =
=
10 9 = 45 .
= = 40 45 = 1350 . 3) : = = 10 = 2 =
. : = = 30 /. : = = 6 . 4) : =
=
= 90
. , : + = 135 .
= 0
1. x
x = 6t (SI) x = 2t2 (SI) . ) .
, :
) t = 2 s ) t = 1,5 s ) t = 3 s 4
) . 8
2. . F :
) .
H
) x0 = 0 m x . ) x x . ) x0 = 0 m x .
4 ) .
9
0 x
F
Ax Bx
Iro Markaki 3
, . F
&
. to = 0 s 2 m/s t1 = 2 s 12 m/s. ( F
&), 2 s
= 98 W. , = 0,2. g = 10 m/s2 .
:
1) ,
5
2) F&
2 s,
6
3) F&
.
7
4) .
7
www.methodiko.net & 2, , : 210 99 40 999 . 201, , : 210 96 36 300
3
- :
1. : ) = ,
= 6 / = 4 /. : = = 4. : = 6 = 4 = 1,5 . 2. : ) = .
, . , . , ( ) ( ). = 0 .
- :
1) , : = + = = = 5 2) : = = 98 2 = 196 . 3) : = +
12 = 2 2 +
12 5 4 = 4 + 10 = 14m
: = = = 14 . 4) : = = 0,2 = 2 = = 14 2 = 5 = 2.
= 2 / = 12 /
= 0 = 2
B 1. xx t = 0 s x0 = 0 m.
.
) .
t = 30 s
) 125 m ) 100 m ) 75 m 4
) .
8
2. .
. 2.
)
:
) 3 ) 2 ) 4 4
)
9
t s0 10
sm /X
10
20
-5
25 30
Iro Markaki 4
m = 10 kg, , t0 = 0 s 1F
& 20 .
1) t0 = 0 s t1 = 10 s. 6
2) 1F&
.
6
t0 = 0 s 1F&
2F&
1F&, .
3)
1F&
2F&
. 5
4) 1F&
t0 = 0 s t1 = 10 s
1F&
2F&
.
2.
8
www.methodiko.net & 2, , : 210 99 40 999 . 201, , : 210 96 36 300
4
- :
1. : ) =
, , . : = = 20 10 = 100 = =
(30 20) 5 = 25 .
: = = 75 2. : )
(....): + = 0 = =
12
12(2) = 3
12 = 3
- :
1) 2 .: = = = 2 /. ,
= 0 = 10 : = = 2 10 = 100 2) : = = 20 100 = 2000 . , : 3) = + = = 4/ ,
= 0 = 10 : = = 4 10 = 200 4) : = = 20 200 = 4000 . : = 2 .
B 1. 1, 2 1 2 ,
.
) 1 2.
5 ) , 1 2 .
7
2. 1, d1 . , 2 = 21, d2.
) . ,
:
) d2 = 2d1 ) d2 = 3d1 ) d2 = 4d1 4
) . 9
1
2
Iro Markaki 5
m = 50 kg . to = 0 s , .
. F = 200 - F = 50 . t1, 2m , , -
.
= 0,4 -
g = 10 m/s2. 1) .
6 2) t1 .
6 3) to = 0 s t2 = 4 s.
7 4) , , to = 0 s t1, .
6
www.methodiko.net & 2, , : 210 99 40 999 . 201, , : 210 96 36 300
5
- :
1. . : 1: = 0 = + 2: = 0 = : = = +
2.
: ) =
. : 0 = =
: =
12 =
12
=
12
=
2
, = 2, : =
2=4
2= 4
- :
1) : = , . : = = 0,4 = 0,4 500 = 200 2) 2 . : = , . : + = 250 200 = 50 = 1 / : =
12
2
= 4 = : = 2 .
www.methodiko.net & 2, , : 210 99 40 999 . 201, , : 210 96 36 300
3) = 0 = . , .. . : = = 2/ ( ). 4) :
= = 200 2 = 400 :
=
= = 200 2 = 400
2
= 0
()
(/)
2 4 2
B 1. , h, h .
) . t = 2t, h h :
) hA = 2hB ) hA = 4hB ) hA = 8hB 4
) .
8
2. ,
a , - .
-
.
) . :
) F1+F2=2mg ) F1-F2=mg ) F1+F2=mg 4
) .
9
m
gm&
1F&
a&m
gm&
2F&
a&
Iro Markaki 6
m = 2 kg . t = 0 s,
F = 10 + 2x (SI). x = 0 m t = 0 s - x. F 50 . 0,4. -
g=10m/s2 .
:
1) .
5 2) x = 10 m.
7 3) F x = 0 m F .
7 4) t = 0 s .
6
www.methodiko.net & 2, , : 210 99 40 999 . 201, , : 210 96 36 300
6
- :
1. : ) = : =
, : = = = 2 .
, : = 4 . 2. : ) + = 2 .. : = (1), : = (2) (1) (2) : ( ) ( ) = 0 + = 2 - :
1) , : = : = = 0,4 20 = 8 2) = 10 : = 30 . : = = 22 = 2 = 11 / , : = 11 /. 3) H : = 10 + 2 50 = 10 + 2 = 20 , . , : = 20 = 600 4) ... =0 . = 0 = 600 8 =
6008
= 75
()
()
20 0
50 10
B1. m = 500 g . F
& 10 N.
) . ,
:
) 20 m/s2 ) 2 m/s2 ) 0,2 m/s2 4
) .
8
B2.
.
) . F
x = 0 m x = 2 m :
) 40 J ) 20 J ) 80 J
4
) .
9
0 x(m )
F( )
1 2
20
10
Iro Markaki 7
. 1) , 2) ,
3) , 4) , 5)
.
( ) , m = 2 kg. ( ) (), F
&
. F = 4 N
1 m 4 s.
( ) .
9 m.
g = 10 m/s2 .. :
1) , ,
6 2) , ( ),
6 3) ,
7 4) .
6
www.methodiko.net & 2, , : 210 99 40 999 . 201, , : 210 96 36 300
7
- :
1. : ) / , ( = =10 ). , : = =
2
=2 10 10
0,5= 20 /
2. : ) ,
. : = = 2 20 = 20
- :
1) (), : = 0 = 0 = = 4 . 4 : =
=
= 0,25 /
: = = = 0,2,
= 0,2. 2) ( ) : = = 4 0,25 = 1 3) (): 9. , : = = =
=
= 2 /.
: =
2 = 2 = 6 /
4) , : = = = 3 .... : = 0
= =
2 6 = 36 . :
. =
= 363= 12
B 1. , , .
) . ,
, , .
(J) (J) (J)
80 100
40
10
4
) .
8
2. F
g2 , g .
) .
, F F .
) F = 2 ) F = 2 ) F =
4
) .
9
Iro Markaki 8
.
1) 1 2 0 s 4 s
8 s 10 s .
5 2) ,
t = 0 s t = 10 s. 6
3) 0 s 10 s. 7
4) 1 2 t1 = 2 s
t2 = 9 s , 12
KK .
7
(m/s)
t (s) 4 8 10
10
20
0
www.methodiko.net & 2, , : 210 99 40 999 . 201, , : 210 96 36 300
8
1. . = + . , , . : 2. : ) =
. , 2 : = =
2 =
2
=2
- : 1) :
0 4 sec : =
=104= 2,5 /
8 10 sec : =
=102= 5 /
.
2) 4 10 s , .
(J) (J) (J) 20 80 100 40 60 100 90 10 100
()
(/)
4 8 2,5
10
5
()
(/)
4 8 10
10
20
www.methodiko.net & 2, , : 210 99 40 999 . 201, , : 210 96 36 300
3) . . :
= + + =12 4 10 + (8 4) 10 +
10 + 202
2 = 20 + 40 + 30 = 90 :
=
=9010
= 9 /
4) = 2 : = = 5/ = 9 : = + = 10 + 5 = 15/ , :
=12
12
=
=
515
=13
=19
1) , () () - 25 km/h. - t = 0 . - .
) , . 25 km/h, : ) ) ) , 25 km/h
4 ) .
8 2) 1 2 1 2 .
) , .
1 = 22, 12
KK
1 2, : ) 4 ) 4 ) 2
4 ) .
9 1 2 m1 = 3 kg m2 = 5 kg , = 0,5. - , . t = 0 1 F - , = = 1 m/s2. 1) .
6 2) 2 - .
6 3) 1, - t = 0 t1 = 4 s.
6
F2. 1.
$%
t
Iro Markaki 9
4) , - 1.
7 g = 10 m/s2.
www.methodiko.net & 2, , : 210 99 40 999 . 201, , : 210 96 36 300
9
1. : )
. , 25km/h. 2. : ) 4
: = = = 2. , :
=12
12
=
=
2
= 4
- :
1) = 0 : = = . = = 15 = = 25 . 2) , (1) , , (2) . () : = 15 = 3 (1) , () : = 25 = 5 (2) (1) (2) : 40 = 8 = 48 = 1/. (1) : 48 15 = 3 33 = 3 = 30.
3) : : =
=
1 16 = 8 . : = = 30 8 = 240
4) : = = 48 8 = 384 : = = 15 8 = 120 ... : = = 384 120 240 = 24 :
100% =24384
100% =116
100% = 6,25%
1) . .
) . : ) . ) )
4 ) .
8
2) h . .
) . 2h, : ) 2 ) 4 ) 2
4 ) .
9 120 kg , xx.. F - t = 0, xo = 25 m, . - = 0,2 g = 10 m/s2. 1) F , , 0 o 5 s.
6 2) F ( F ), - t1 = 3 s.
6 3) t2 = 10 s.
6 4) F , 4 .
7 g = 10 m/s2.
x
t1t
1x
0 5 10
20
(s)t
(m/s)
15
10
Iro Markaki 10
www.methodiko.net & 2, , : 210 99 40 999 . 201, , : 210 96 36 300
10
1. : )
. , . . . 2. : )
: = = 2 : =
2 2 =
2 2
2=
2 = 2 = 2
- :
1) = 0 = 4 , : = 0 = = = = 0,2 1200 = 240 2) ( ) : =
= = 240 10 = 2400
3) . : = + = 10 5 +
(20 + 10)2
5
= 50 + 75 = 125 : = = + = 125 25 = 100
4) 4 sec = = 10 : = = 240 10 = 2400
()
(/)
5 10
10
20
15
1) m () F , .
) . 2m, -:
) 2 ) 3 ) 2a
4 ) .
8 2) 1 , H , . - ,
, 2Hh
. - .
) . : ) . ) .. ) .
4 ) .
9 1 2 40 kg -, -. t = 0 1 - 2 40 m/s, - 1. . 1) - 1 .
6 2) , t1, , t2 = 15s.
6 3) t1.
6 4) t = 0, - .
7
0 1t
60
(s)t
(m/s)
15
40
1
2
Iro Markaki 11
www.methodiko.net & 2, , : 210 99 40 999 . 201, , : 210 96 36 300
11
1. : )
: = = . A
. : = 2 =
12 =
12
2. : ) .
: 0 = : = = = : 0 + = + = , . - :
1) () : =
= 4/ , : = = 160 . 2) () =15 :
=12 0 =
12 40 3600 = 72.000
() : = 0 . 3) : =
= 450 = 40 15 = 600 . , : = | | = 150 ( .) 4) = 15 () = 15 . : = . 40 = 450 + 60( 15) 40 = 450 + 60 900 450 = 20 =
= 22,5 22,5 .
1) . .
) . : ) . ) )
4 ) .
8 2) () () - . - .
) . () (), - , : ) () ) () ) , .
4 ) .
9 1 2 m1 = 6 kg m2 = 4 kg , 2 1. t = 0 1 F - . , . 1 30 g = 10 m/s2. 1) F .
5 2) F , - 120 m.
6 3) 1 .
6 4) t1 2, F 1 10 m/s. 1, t2 = t1 + 5 s.
8
x
t1t
1x
F1626
Iro Markaki 12
www.methodiko.net & 2, , : 210 99 40 999 . 201, , : 210 96 36 300
12
B1. : )
. , . . . B2. : ) , . : = ,
= , ,
: =,
: = , . : =
,
. , > , > .
- : 1) : = 0 = = 30 . 2) = 120 . : = = 30 120 = 3600 3) : + = (1) : = : = (1) : + = = ( + ) = 100 = =
= 0,3 4) : = 10/ . : = = = 0,3 60 = 18 = = 12 = 6 = 2/ , : = + , = , . , = + 5 = 5 : = 10 + 2 5 = 20 / : =
=
6 400 = 1.200
1) , t = 0 - .
) . t1 1, - t2 = 2t1 : ) 21 ) 41 ) 1
2
4 ) .
8 2) () m 1,2 m ( 1). 4 m ( 2).
) . W1 W2 (1) (2) , : ) W1 = W2 ) W1 < W2 ) W1 > W2
4 ) .
9 900 kg - , - xx. to = 0, , xo = + 25 m. - , t = 0 t4 = 25 s. 1) .
5 2) , t = 0 t1 = 5 s.
6 3) t2 = 15 s t4 = 25 s.
6 4) , - t = 0 t4 = 25 s.
8
0
20
(s)t
(m/s)
15
10
20 255
20
Iro Markaki 13
www.methodiko.net & 2, , : 210 99 40 999 . 201, , : 210 96 36 300
13
1. : )
: = , : = : = = 2 = 2. 2. : ) <
( < 0) ( = 0).
- : : = 20 15 = 5 , . = 20 . 2) 0 5 , : =
=
= 2 / : = = 1800
3) . 0 15 : =
20 + 102
5 + 20 10 = 275 : = = 25 + 275 = 300 15 20 : = = = 50 20 25 : = =
= 50. ,
( = = 300 ) . , , . , 15 25 . 4) .... : = = = 900 [(20) 10] =
12 900 (400 100) =
12 900 300 = 135000 .
()
(/)
5 15 10 20
25 20
20
1) 1 , H , . . , . - - .
) . : ) . ) . ) .
4 ) .
8 2) , 1 2 , .
) . t = 0 t1, - 1, : ) 2. ) 2. ) 2.
4 ) .
9 8 kg . t = 0 F , - xx. - x , 100 20F x , ( F x m) . x = 0 30 . 1) F .
5 2) F , t = 0, .
6 3) F .
6 4) , - F .
8
t1t
1
1
2
0
12
Iro Markaki 14
www.methodiko.net & 2, , : 210 99 40 999 . 201, , : 210 96 36 300
14 :
1. : ) .
, . , .
2. : ) .
, : . : =
= 2 = 2
- :
1) : = 0 100 20 = 0 = 5 . 2) , . =
100 5 = 250
3) ... = 5 : =
12 0 = 250 30 5 4
= 100 = 5/ 4) . = 30 30 = 100 20 20 = 70 = 3,5 . = 5 = = 1,5 .
()
(/)
2
()
() 100
5
1) - , - xx. - .
) . : ) 140 m ) 60 m ) 40 m
4 ) .
8
2) F . x, .
) . 4F x, : ) 2 ) 4 )
2
4 ) .
9 m = 20 kg, . to = 0 1 2, F F 3F . 1 2, F F , - 35 45 , , 3F , - . 1 2, F F , - t1 = 6 s 45 m. : 1) 0 o t1.
6 2) 3F .
6 t1, . . to = 0, t2 = 10 s, - 137 m. 3) .
8 4) 0 o t2.
5
t s0
x m
5 10 15 18
50
40
Iro Markaki 15
www.methodiko.net & 2, , : 210 99 40 999 . 201, , : 210 96 36 300
15 :
1. : )
= 0 = 15 = 0. = 18 =40 . : = = 40 0 = 40 2. : )
, .... : =
12 0 = =
2
= 12 0 = 4 =
2 4
: = 4 = 2. - :
1) : = 45 =
36 =
= 2,5 /
2) : = 35 + 45 = 20 80 = 50 = 30 3) = 6 = 10 : = 137 45 = 92 . : = = 2,5 6 = 15 / : = +
92 = 15 4 +
16 92 60 = 8 = 4 /
, : = = 80 = + . 4) : = + = 15 + 16 = 31 / ... : = =
12 20 31 0 = 10 961 = 9610
45
1) , - . , - , .
) . g , : ) MgH. ) MgH. ) MgH.
4 ) .
8 2) - -, .
) . s s, , 10 to , : ) As s% ) 2s s$ ) A 2s s%
4 ) .
9 1 2 , m1 = 15 kg m2 = 25 kg . - l = 2 m, - . t = 0 1 F 2 m/s2, . - = 0,4. 1) ..
6 2) 2 2 .
6 3) F , t = 0 t1 = 4 s.
6 4) t1 = 4 s , F . - 1 2, t2 = 7 s.
7 g = 10 m/s2.
F26 16
t1t
1
A
0
Iro Markaki 16
www.methodiko.net & 2, , : 210 99 40 999 . 201, , : 210 96 36 300
15 :
1. : ) .
. , . ( : = + = 0 + = ). , , . . 2. : ) = .
: =
, : = .
: =
= = . , = . = : = = 2. - :
1) : = = = 150 = = = 250 . : = = 0,4 150 = 60 = = 0,4 250 = 100 2) () : = = + = 100 + 25 2 = 150 . , 150 . 3) = 0 = 4 . : =
=
2 16 = 16 .
() : = = 150 + 60 + 15 0,4 = 216 . : = = 216 16 = 3456
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4) () . : = 216 60 = 15 =
= 10,4 / = = 8 /. () = 4 = 7 : = +
= 8 3 +
10,4 9 = 70,8 (1), = 7 4 = 3 .
() = = = 4/ : =
(2)
(2) . . : = , . = 0 : = = = 2 . 6 s : =
= 8 2
4 2 = 8 T : = + = 2 + 70,8 8 = 64,8 .
: !
= = s
=