s , | j - , j = 2p N; (N ) | |
u - - (/) u = d s /d t = s¢ | w- , / w = 2p n; w =dj/ dt = j¢ (n /) | |
a - , /2 a = du/d t = u¢ | e - . , /2 e = dw/d t = w¢ | |
<u>=D s/ D t < a >=Du / D t | <w>=DjD t <e>=Dw/D t | |
u -const s = u t | w - const j = w t | |
a = Du/D t s = u0 t at 2/2 u = u0 at | e = Dw/D t j = w0t e t 2/2 w = w0 e t | |
a n = u2/ R a t = du/d t a = Ö a t 2 + a n 2 | ||
- , , . . 2π. w = j/ t = 2π./
= 2π./ w.
j(t), w(t), e(t) , (.4, 5).
.
1. s, , t s = 4 t 2 t 2 + t 3 (s , t ). : 1) u t; 2) , , ; 3) .
. 1) . , .. (2), - , ..
u(t) = s ¢= 4 - 4 t + 3 t 2; (t) = u¢ = s¢¢ = -4 + 6 t ×
2) , , :
s =4×3 - 2×32 + 33 = 9 ; u = 4 - 4×3 + 3×32 = 10 /; = -4 + 6×3 = 14 /2.×
3) <u> <u> = D s / D t, D t = t 2 -t 1, D s = s2 s1. t 1= 0, t 2= 3 , D t = 3 ;
s 1= 0, s 2= 4×3 - 2×32 + 33 = 9 . <u> = 9 / 3 = 3/
< a > < a > = Du / D t, D t = 3 , Du = u2 u1. t 2 t 1 u(t) = s ¢= 4 - 4 t + 3 t 2, t 1=0 u1=4 /, t 2= 3 u2= 19 /, < a > = (19 4) / 3 = 5 /2.
2. . 10 (1, 2, 3). : (, , ); u0; a; , .
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. 1 , u0 12 /, a =(u - u0)/D t. :
a = (0 - 12) / 6 = -2 /2.
- (12), :
s 1= 12×6 - 2×62/2 = 36 ,
u(t)
s 1= 12 × 6 / 2 = 36 .
2 u0 = 4 /. 8 12 / ( u),
a = (12 - 4) / 8 = 1 /2.
(12)
s 2 = 4 × 8 + 1×82/2 = 64 .
, 2 64 .
3 , u = 12 / 3 = 4 /. u0 = 4 / , 4 /.
a = (4 - 12) / 4 = -2 /2.
, , s = u× t = 12 × 4 = 48 s = 12 × 4 2 × 16 / 2 =32 .
s = 48 + 32 = 80 .
3. 10 , j = 3 + 2 t + t 3 (j , ). 1) ; 2) ; 3) ; 4) ; 5) ; 6) ; 7) .
. 1) : j = 3 + 2×3 + 33 = 36 . j N j = 2πN, .. N = j / 2π, N = 36/6,28 = 5,73 .
2) w = j¢ =2 + 2 t 2, w =2 + 2×32= 20 /. w = 2π n, n = 20 / 6.28 = 3,18 /.
3) u = w× R, .. u = 20×0,1 = 2 /.
4) e = w¢ = 4 t, .. e = 4×3 = 12 /2.
5) n = u2/ R = w2× R, .. n =202×0,1= 40 /2.
6) t = du/d t = u¢ = e× R, . . t = 12×0,1 = 1,2 /2.
7) ,, ..
= Ö 402 + 1,22 = 40,02 /2.
4. 300 u0 = 600 /. 20 1) ( ); 2) ; 3) ; 4) ; 5) . g = 10 /2
. .2. , : u = u0 = u0×cosa, - u0= u0×sina g = 9,8 /2. :
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: = u0×cosa× t, (25)
: y = u0×sina× t gt 2/2, (26)
u = u0×sina gt. (27)
, g ( , ).
. 1) t = 20 ( , , t1). t t1, , . t (27).
u = u0×sina g t1 = 0,
t1 = u0×sina / g. t1 = 600×sin300 /10 = 600×0,5 /10 = 30 c.
t t1, t < t1, .
2) t =20 = h. h (25): h = u0×sina× t gt 2/2;
h = 600×sin300×20 - 10×(20)2/2 = 6000 2000 = 4000 .
3) , . 11, : u = Ö ux2 + uy2. u (27) 20: u = 600×0,5 10×20 = 100 /. , u = 600×cos300=600×0,87=520 /c, u = Ö1002 + 5202 = 529,53 /
4) n g, , n. . 12. , .. . . 11 , sinb = u / u = n / g;
sinb = u / u = 520 / 529,43 = 0,98; b = 790.
5) b, t n: t = g×cosb; t = 10×0,71 = 7,1 /2;
n = g×sinb; n = 10×0,7 = 7 /2
5. , , t = 15 c , n = 600 /. t.
. , ,
j = 2πN = w0 t + e t 2/2; w = w0 + e t.
w0 , w = e t. , w = 2π n, 2π n = e t. e = 2π n / t. / /: n = 600/60 = 10 /. e = 2×3,14×10/15 = 4,2 /2.
(w0=0), , N = e t 2/(4π). 6
N = 4,2×102/(4×3,14) = 420 / 12,57 = 33,41
.
. , . , .
4,5, 9, 10, . . . (, 14, 15, 16) , , .. .
.
, , .
1. (, . ).
2. (, . ).
3. (, . , ).
4. /2 (*2, *, ..)?
5. ?
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6. , 0,1 /2 . ?
7. 3 /. .
8. 0,5 /2. .
9. , τ = 0, n = 2 / 2 .
10. : τ = 0, n = const?
11. , n = 0?
12. , , . .
13. () ..
14. s = 0,3 t 2 + 0,1, (/). .
) ; ) ; ) ; ) ; ) ? .
15. . , ( - ; υ - ; - ):
) = 3 t 4 + 1; ) υ = 3 t 2 + 2 t; ) = 0,1 + t; ) = 0,3 t 2 + 0,1;. ) .
16. ?
) υ = 5 + 2 t 2 ; ) s = s 0+ 2 t; ) s = 2 t 2; ) s = s 0- 2 t - t 2;
) υ = 3 - 2 t; ) a = 0.5 t.
17. s = 3 t 2 + t + 1. .
18. υ = 1 + 2 t 2 ,/. . x (t).
19. , , (.13). ?
20. 10 , 5,4 /?
21. . 0,1 /2, . ?
22. 4 /. 2 /. , ?
23. 40 /, - 30 /. ?
24. , (.14). ?
25. s = 5 t + 0,4 t 2. 3 . 3 ?
26. υ = 3 + 4 t 2,/. 2 .
27. a = (2 t 2 + 0,5 ),/2. ?
28. . . 50 /, 70 / 60 /. .
29. , , 100 10 , 300 - 15 . .
30. υ = 20 - 2 t. 3 ?
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31. , , s = 2 + 3 t, t - . ?
32. (.15), () . υ - ; S - ; a - ; t - .
33. .
34. 10 / 2, 9 /2. .
35. () (.16) . (, ) .
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36. 1 /2, .
37. , . 2 . υ = 5 + 6 t 2,/. .
38. 20 , 36 / 0,2 /2. ?
39. . 1 (.18 ), - 2 (.18 ). ?
40. 100 . 0,2 ?
41. 100 . 10 ?
42. 5 10 . ? .
43. 20 /, - 40 /. .
44. , 40 / 2 . ? ?
45. , 20 , 15 . . .
46. 10 / 60˚ 1 . , 30 ?
47. 30˚ 5 /. .
48. , 800 / 1 . , ?
49. , , . υ1 υ2 (.19). ?
50. . 0,7 , - 0,5. 10 /, - 15 /. ?
51. 1 2 /. .
52. 30 5 /. ?
53. (.20).
1) 1 2) 2 3) 3 4) 4
54. 2 / 1 . , ?
55. , .21. ( )
1) 1 2) 2 3) 3 4)
56. φ = 3 t 4 + 1. 1 .
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57. w = 0,3t2 + 0,1, (/). ) ; ) ; ) ; ) ; ) ? .
58. φ = A + Bt + t 2, = 10 ; = 4 /; = -1 /2. , 1 t = 4 .
59. 2 , 10 . .
60. , 2 10 . .
61. 2 , 10 . .
62. 1 0,1 2 (.22). 2. , , 2.
63. ε = 0,15t. .
64. , (.23). ε(t) φ(t). φ0 = 0.
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65. , 2 .
66. 10 -1 2 -2. 5 ?
67. : υ, - 2υ . ?
68. . s = 2 + 0,5 t 2,. , t = 1 . 50 . 1 ?
1