.


:




:

































 

 

 

 


2

 

1. -, r = 3 t 2 i + 2 t j + k, i, j, k x, y, z. v t = 1 .

2. , x = At, y = Bt + Ct 2, A = 2 /, B = 2 /, C = 1 /2. 10 .

3. r (t) = A (i cosw t + j sinw t), A = 0.5 , w=5 -1. . v n.

4. x x = A cos(2p t / T), = 8 . x v a , vx t 1 = 0 t 2 = T /8.

5. x 0 y x = At, y = At (1 - Bt), A B . , , . .

6. x 1= A 1+ B 1 t + C 1 t 2; B 1 = 4 /, C 1 = - 4 /2, x 2 = A 2+ B 2 t + C 2 t 2; B 2 = 1 /, C 2 = 0.5 /2. te, . .

7. t = 0 x. v = v0 (1 - t / T), v0 - , v 0 = 0.1 /; T = 5.0 . t 1= 8 .

8. x = A + Bt + Ct 2 + Dt 3, A = 0.1 , B = 0.1 /, C = 0.14 /2, D = 0.01 /3. 10 .

9. T = 4 v = At 2 + Bt, A = 2 /3, B =4 /2, (0 ≤ tT). , .

10. . t = 4 L = 40 . v 0 vf .

11. x 0 y x = A sinw t, y = A (1 - cosw t), A w . , , .

12. v0 = 30 / 600 . .

13. vx = A wcosw t; vy = A w sinw t; vz = 0, A = 15 w = 3 -1 . .

14. . m 1 = 2 , m 2 = 4 . k = 0.3. , ?

15. 1, 2 3, , , (.). . . , .

16. , (.). m1 ; . 2. a T ? α.

17. . , , , . ?

18. , 4 /, , = 5√ v (/). .

19. , φ = + t + t2 , = 2 /; = 1 /2 2 .

20. , φ = 0,5t2 (). , 80 .

21. 10 , φ = + t + t2 + Dt3, = 1 /, = 1 / 2, D = 1 /3. .

22. 2 , s = 0,1 t3 (). , 0,3 /.

23. , φ = + t + t2 + Dt3, = 1 /, = 1 / 2, D = 1 /3. , 1,8 /2 .

24. , 4 , n = 1 + 6t + 9t2 (/2). 1 .

25. , φ = 0,5 t2 (). , 80 .

26. 10 , v = 3t + t2 (/) 1 .

27. , s = t + Ct2, = 2 /, = 1 /2. 2 0,5 /2. 3 .

28. 2 = 10 Cos πt (/). - . - 1/3 .

29. 2 s = 5 Sin πt (). , .

30. 1 = t + Ct2 Dt3, = 2 /2 D = 0,4 /3 . , .

31. 1 - r0 = 2 i + 3 j, i, j x, y. F = 1,5y2 i + 3x2 j 0,2(x2 +y2) k. .

32. 100 , 200 , ,1000 90 . , 10 ?

33. m , 2m. .

34. 5 , v = √ s (/). , 15 .

35. (ρ = 1,29 /3) 0,55 2 20 /. ?

36. r Wp (r) = r -3 . , (0,4; 0,5; 0,6).

37. 2 8 / 3 , 4 /. .

38. , , . 36 , 144 . .

39. R = 3 , j = A + Bt + Ct 2 + Dt 3, D = 1 -3. D a t .

40. e = 2 -2. t = 0.5 a = 15 /2. .

41. t = 10 R = 5 a = 15 /2. , t = 5 .

42. R = 15 . a n = 4.9 /2, 600 . v a t .

43. R = 5 , S = A + Bt + Ct 2, B = - 2 /, C = 1 /2. , t = 3 .

44. x = A 1 t 3 y = A 2 t A 1 = 2 /3, A 2 = 2 /. 0.8 .

45. x 0 y x = A sinw t, y = B cosw t, A, B w , A = B = 5 c. , , .

46. R L = A sinw t, L , , A w . L = 0.

47. R = 5 L = At 3, A = 2 /3, L , . ? .

48. e = - 3 -2. N , n 1 = 240 -1 n 2 = 90 -1, D t, .

49. a t= 0.5 /2. , R = 4 , v = 2 /.

50. R = 10 v = At, A = 0.5 /2. , L, 0.1 .

51. vx = A wcosw t; vy = A w sinw t; vz = 0, A = 10 w = 3 -1 . .

52. R = 1 , j = A + Bt + Ct 3, B = 2 -1, C = 1 -3. D t = 3 .

53. R = 0.5 , , , , . a = 5 /2 . .

54. R = 0.2 . t = 20 w = 20-1 N , , .

55. R = 15 a t. , , v = 79.2 /.

56. , j = A + Bt + Ct 2 + Dt 3, B = 1 -1, C = 2 -2, D = 1 -3. , , , , a n= 3.46.102 /2.

57. , , v 1= 2 / v 2= 6 / s = 15 . F = 2 . m = 1 .

58. (3, 10, 8) 1 (1, 2, 3) 2 (3, 2, 1) . ? ?

59. v = 50 / α = 150. , , N = 20 .. (1 .. = 736 ). , 1200 .

60. L 0 , , - , . v? μ.

61. . u . w ? v ? .

62. , , l. S1 S2 ?

63. 3×102 / 6×102 / . , 3 . .

64. ( l) . u , , : ) ; ) .

65. m1 m2 v1 v2. , . , . , .

66. , V, , 4 . , , , 600. . .

67. . , , . () ? , .

68. 0,03 , . v () . η = 14 -/2, dx = 1,26 /3, d 2 = 7,8 /3. (1 = 10-5 ).

. , , , : f=6πrvη.

69. 0,6 (ρ = 1,3 /3, ŋ = 10 5 ). , .

70. (ρ = 7900 /3) 5 (ρ = 900 / 3 ŋ = 1 ). .

 

 



<== | ==>
, | . , ,
:


: 2016-09-03; !; : 954 |


:

:

- - , .
==> ...

931 - | 973 -


© 2015-2024 lektsii.org - -

: 0.048 .