1. x 0 y x = At, y = At (1 - Bt), A B . , , . .
2. R = 5 , j = A + Bt + Ct 2 + Dt 3, D = 1 -3. D a t .
3. e = 2 -2. t = 0.5 a = 13.6 /2. .
4. t = 10 R = 10 a = 15 /2. , t = 5 .
5. x 1= A 1+ B 1 t + C 1 t 2; B 1 = 2 /, C 1 = - 4 /2, x 2 = A 2+ B 2 t + C 2 t 2; B 2 = 2 /, C 2 = 0.5 /2. te, . .
6. R = 10 . a n = 4.9 /2, 600 . v a t .
7. t = 0 x. v = v0 (1 - t / T), v0 - , v 0 = 0.1 /; T = 5.0 . t 1= 6 .
8. R = 10 , S = A + Bt + Ct 2, B = - 2 /, C = 1 /2. , t = 3 .
9. x = A + Bt + Ct 2 + Dt 3, A = 0.1 , B = 0.1 /, C = 0.14 /2, D = 0.01 /3. 12 .
10. x 0 y x = A sinw t, y = B cosw t, A, B w , A = B = 4 c. , , .
11. R L = A sinw t, L , , A w . L = 0.
12. T = 4 v = At 2 + Bt, A = 2 /3, B =4 /2, (0 ≤ t ≤ T). , .
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13. x = A 1 t 3 y = A 2 t A 1 = 1 /3, A 2 = 2 /. 0.8 .
14. R = 2 L = At 3, A = 2 /3, L , . ? .
15. . t = 2 L = 40 . v 0 vf .
16. x 0 y x = A sinw t, y = A (1 - cosw t), A w . , , .
17. v0 = 20 / 600 . .
18. e = - 2 -2. N , n 1 = 240 -1 n 2 = 90 -1, D t, .
19. a t= 0.5 /2. , R = 3 , v = 2 /.
20. R = 12 v = At, A = 0.5 /2. , L, 0.1 .
21. vx = A wcosw t; vy = A w sinw t; vz = 0, A = 12 w = 3 -1 . .
22. R = 1 , j = A + Bt + Ct 3, B = 2 -1, C = 1 -3. D t = 2 .
23. R = 0.5 , , , , . a = 6 /2 . .
24. R = 0.1 . t = 20 w = 20-1 . N , , .
25. R = 10 a t. , , v = 79.2 /.
26. -, r = 3 t 2 i + 2 t j + k, i, j, k x, y, z. v t = 1 .
27. , x = At, y = Bt + Ct 2, A = 1 /, B = 2 /, C = 1 /2. 10 .
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28. r (t) = A (i cosw t + j sinw t), A = 0.5 , w=5 -1. . v n.
29. x x = A cos(2p t / T), = 8 . x v a , vx t 1 = 0 t 2 = T /8.
30. , j = A + Bt + Ct 2 + Dt 3, B = 1 -1, C = 1 -2, D = 1 -3. , , , , a n= 3.46.102 /2.
31. , , v 1= 2 / v 2= 6 / s = 10 . F = 2 . m = 1 .
32. (3, 10, 8) 1 (1, 2, 3) 2 (3, 2, 1) . ? ?
33. m 1 = 0.2 . , m 2 = 0.3 , . k = 0.25. . .
34. , . , k = 0.25?
35. . m 1 = 2 , m 2 = 4 . k = 0.25. , ?
36. 1, 2 3, , , (.). . . , .
: ; ; ;
37. , (.). m1 ; . 2 a T ? α.
:
38. v = 50 / α = 160. , , N = 20 .. (1 .. = 736 ). , 1200 .
: Nmax = 81,2 ..
39. L 0 , , - , . v? μ.
: v = ½(μgL)1/2
40. . u . w ? v ? .
:
41. , , l. S1 S2 ?
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:
42. 3×102 / 5×102 / . , 3 . .
43. ( l) . u , , : ) ; ) .
: v2 ≥ 4 gl; v2 ≥ 5 gl
44. (α ) ; μ α. . , m. ?
45. , α , . , V, v , , . τ, . μ. μ ?
: τ = (1/2g)(((V-μvcosα)/(μcosα sinα)) v); μ ≤ tgα + (V/vcosα))
46. m1 m2 v1 v2. , . , . , .
: = (1/2) (m1m2/(m1 + m2)) (v1 v 2)2)
47. , V, , 3 . , , , 600. . .
: V1 = V (13)1/2/4; V2 = V/ 4
48. . , , , . ?
: ; 900.
49. . , , . () ? , .
: √2 .
50. 0,05 , . v () . η = 14 -/2, dx = 1,26 /3, d 2 = 7,8 /3.
. , , , : f=6πrvη.
: