2015 - 2016

1

4 . 691) 4 .

4 . 69

6 . 692) 6 .

6 . 69

1 :

, ..., .

t1 = 5 s, x1 = 20 m , t2 = 10 s, x2 = 40 m, :

) = ; , : ,

) x = ; , t3 = 25 s t4 = 40 s ,

) , ( x t )

, ( t ),

.

:

)

= ....

=

)

x = .

x = .)

2 : 0 = 4 m/s , ...., .

= 2 m /s2) , t1 = 3 s, x1 = ;

1 = t1 + t1 => 1 = + ( . ) => 1 = + . => 1 = + => 1 = m) t0 t2 = 2 s,

, ;

= 2 m /s22 = t2 - t2 => 2 = - ( . ) => 2 = - . => 2 = -

=> 2 = m) , = 2 m /s2 t3 = 10 s,

x3 = ;

3 = t3 + t3 => 3 = + ( . ) => 3 = + . => 3 = +

=> 3 = m) - . ( ) )

( . 69 - 70 )

7 : : = 2 m/s2 t = 15 s = 0 m/s. = + t => = .. => = . m/s

0

. s = t + t => s = t => s = ( . ) => s = . . => => s = m 8 : : = 20 m/s t = 10 s = 0 m/s

. s = = = t = .. . => s = .. => s = . m . ,

, :

:

0 s = t + t => s = t

1 , ( t1 = 1 s ), 0

s1 = t1 + t1 => s1 = t1 => s1 = ( ) => s1 = . .=> => s1 = m 2 , ( t1 = 2 s ), 0

s2 = t2 + t2 => s2 = t2 => s2 = ( ) => s2 = . . =>=> s2 = m :

s = s2 - s1 = .. - . = m 9 : : = 20 m/s t = 30 s t = 10 s

. s = = ( + ) /2 = ( + ) /2 = /2 = => s = . m

. = s / t = . / .. = .. m/s ( . 70 - 71 )

16 : : = 9 m/s t1 = 3 s t2 = 5 s t3 = 3 s

. S = = 1 + 2 + 3

1 = = t1 = .. .. = .. => 1 = m

2 = = t2 =.. .. => 2 = .. m3 = ( 1 + 2 ) = ( 1 + 2 ) t3 = ( .. + .. ) = .. .. = .. ..

=> 3 = mS = 1 + 2 + 3 = .. + . + . => S = . m

t = t1 + t2 + t3 = .. + .. + .. = s

= S / t = .. / .. = .. m/s

. 3s : = / t = ( ) / ( t t ) = ( .. .. ) / ( .. .. ) = / = . m/s2 3s :

= / t = ( ) / ( t t ) = ( .. .. ) / ( .. .. ) = / = . m/s2 19 : : o = 10 m/s t1 = 5 s t2 = 10 s t3 = 5 s t4 = 5 s . S = = 1 + 2 + 3 + 4

1 = ( 1 + 2 ) = 2 = =

3 = =

4 = = S = t =

= S / t = .. / .. = .. m/s

. 5s : = / t = ( ) / ( t t ) = ( .. .. ) / ( .. .. ) = / = . m/s2 . S = = 1 + 2 + 3 + 41 = = t1 = .. .. = .. => 1 = m

2 = = t2 =.. .. => 2 = .. m3 = ( 1 + 2 ) = ( 1 + 2 ) t3 = ( .. .. ) = .. .. = .. ..

=> 3 = m3 = ( 3 + 3 ) = ( 3 + 4 ) t3 = ( .. .. ) = .. .. = .. ..

=> 3 = mS = 1 + 2 + 3 + 4 = .. + . + . + . => S = . m t = t1 + t2 + t3 + t4 = .. + .. + .. = s = S / t = .. / .. = .. m/s ( . 70 - 71 )

10 : : = 8 +2t m/s t1 = 2 s t2 = 4 s

. = 8 + 2t = 0 + t, 0 = 8 m/s = 2 m/s2 . :

s = t + t

2 , ( t1 = 2 s ), s1 = t1 + t1 => s1 = .. .. + .. ( .. ) => s1 = .. + .. .. =>

s1 = .. + .. => s1 = m ( 1 )

4 , ( t2 = 4 s ), s2 = t2 + t2 => s2 = .. .. + .. ( .. ) => s2 = .. + .. .. =>

s2 = .. + .. => s2 = m ( 2 )

:

s = s2 - s1 = .. - . = m

12 : : d = 200 m t = 10 s = 30 m/s

d t1 t2t = t2 - t1 = t . :

= + t => = + t => .. = + .. ( 1 )

s = t + t => d = t + t => .. = .. + ( ... ) =>

.. = .. + ... => .. = .. + ... ( 2 )

11 : : t = 10 s 1 = 50 m/s 2 = 30 m/s

B. ( )

= ( t ) . t =.. s = .. m/s. B.

s1 10 , ( t = 10 s ).

1 1, :1 = 1 => 1 = t 1 => 1 = .. .. => 1 = .. => 1 = m

s2 10 , ( t = 10 s ).

2 2, :

2 = 2 => 2 = t 2 => 2 = .. .. => 2 = m s :

s = s2 - s1 = 1 - 2 = .. - . = m . ,

1 = 2, t.

1 = ( + ) 11 = 2 = 2

1 2 10 t

1 = 2 => ( + ) 1= 2

1 = ( + ) 1 => 1 = [( t + ( t 10 )] 1 => 1 = [( .. + ( .. 10 )]

=> 1 = ( .. 10 ) (1) => 1 = t + (1)

2 = 2 => 2 = .. t => 2 = .. t (2)1 = 2 => ( + ) 1= 2 => (1) = (2) => t + = .. t => => .. t = . => t = 17 : : 0 = 10 m/s = 2 m/s2

. : = / 2 :

= - t => / 2 = - t => .. / 2 = .. - .. t => .. / 2 = .. - .. t

=> .. = .. - .. t => .. - .. = .. t => .. = .. t => t = .. s

2,5 , ( t = 2,5 s ) :s = t - t => s = . . - . ( . ) => s = .. - . . => s = .. - . . => s = .. m

B. = - t = 0 m / s : = - t => 0 = - t => = t => / = t => .. / .. = t => t = .. s

13 : : 0 = 72 Km/h => 0 = 20 m/s = 10 m/s2 t1 = 0,7 s d = 50 m

s = t => s1 = => s1 = .. m

s = d - s1 => s = .. - .. => s = .. m ( )

: : = - t

: 0 = - t :

= - t => 0 = - t => = t => t = / ( 1 )

: s = t - t ( 1 ) :

s = t - t => s = ( / ) - ( / ) => s = 2 / - / => s = 2 / - / => s = 2 /

:

s = 2 / => s = (.. )2 / => s = m ( ) () () . 2

1.2.1 :

1) ;

2) ;

)

)

3) ;

)

)

)

1.2.2 : 4) ;

5) ;

6) ; :

7) ; : : = 20 cm F = 80 N

A. Hooke : F = K x

: 80 = . 20 = . / . = 4 / cm :

( cm )

( N )

.

()

( cm )

. . :

= . = .. / .. = .. / cm,

. 1 : : F = 80N F = 60N

. 0 : F = F1 + F2 => F = .. +.. => F =

:

B. 180 : F = F1 - F2 => F = .. - .. => F =

:

2 :

. F = F1 + F2 - F3 => F = .. +.. -. => F =

:

. F = F1 - F2 - F3 => F = .. - .. - . => F =

:

. F = F1 + F2 + F3 => F = .. +.. + . => F =

:

3 : : F = 10N . F1 = 4 F2 => F = 4 F2 + F2 => F = 5 F2 => F / 5 = F2 => . / 5 = F2 => F2 = F1 =4 F2 => F1 = 4 . => F1 =

:

. F1 =3 F2 => F = 3 F2 - F2 => F = 2 F2 => F / 2 = F2 => / 2 = F2 => F2 =

F1 =3 F2 => F1 = 3 . => F1 =

:

5 : : F = 22 N F = 7 N

F1 - F2 - F3 = 0 => F3 = F1 - F2 = .. - => F3 = . N

:

6 : :