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1-6 ??r???r ?????
drdrdvdv?????? ?????????????dtdtdtdt
??????
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??
?r???????r???????????r?r2?r1??r?r2?r1?
?2?
dsdrdr
???????. ?v?
dtdtdt
dr
???????????. dt
????r?????????r?rr??
??
?drdrdr
??r ?r
dtdtdt
dr
??????????? dt
?
drdr
?????1-1???.dtdt
?1-6?
?
dvdv?dv
(3)?????????a??????a???????.
dtdtdt
??v?v?(???????????????
??
??dvdv?d????v dtdtdt
dv
??????????. dt???d??dr?(????????????????????) dtdt
??
1-7 ?????????x=x(t)?y=y(t)???????????????????
drd2r?r?x?y?????v =??a?2??????????????????
dtdt
2
2
??????????????
dx??dy?=??????a=
dt???dt?
22
?d2x??d2y?
??dt2?????dt2?? ??????????????
22
??????????????
???
?????????.????????????????????????r?xi?yj?
?
?drdx?dy??v??i?j
dtdtdt
?222
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a?2?2i?2j
dtdtdt
???????
?dx??dy?22
v?vx?vy??????
?dt??dt?
2
2x
2y
22
?d2x??d2y?
a?a?a???dt2?????dt2??
????
2
?????????????????????????????????????
dr
v?
dt
d2ra?2
dt
drdrd2r
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dtdtdt
d2r
????????????????2?????????????????????
dt
2
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?????a??2?r????????????????????r????????
dt?dt?????
??
????????????????????r???v???????????????
?????
1-8 ????xOy???????????
x=3t+5, y=
12
t+3t-4. 2
??t? s??x,y?m??(1)???t?????????????????(2)??t=1 s ???t?2s ???????????1????????(3)??t?0 s???t?4s?????????(4)??????????????t?4 s ???????(5)??t?0s ?t?4s ??????????(6)????????????????t?4s ???????(?????????????????????????????????????????????)??
?12??
???1? r?(3t?5)i?(t?3t?4)jm
2
(2)?t?1,t?2??????
???
r1?8i?0.5j m
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r2?11j?4jm ?????
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(3)?r0?5j?4j,r4?17i?16j
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??
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????????rr4?r012i?20j
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dt
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??????
(5)? v0?3i?3j,v4?3i?7j
?????vv4?v04???1jm?s?2 ??t44
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???????y????????????
? ?????h???????????????????S????1-4???????
v0(m2s?1)???????????????????????
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2
2
2
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2sdtdt
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dlds?v0,v??? ? v???dtdt
2l? v???
???
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lv0(h2?s2)1/2v0
?? v?? ss
?v???t??????????
dlds
?ldv?v0s?lv?
a???dt2dtv0?v0
2
dtss
l22
(?s?)v02
h2v0??3
s2s
s
1-9 ???x??????????????? a?2+6x?a????m?s?x???? m. ???x?0?????10m?s,??????????????? ?? ?a?
?1
2
?2
dvdvdxdv
??v dtdxdtdx
2
????? ?d??adx?(2?6x)dx ?????
12
v?2x?2x3?c 2
????x?0??v0?10,?c?50
? v?2x3?x?25m?s?1
1-10 ???????????????? a?4+3t m?s???????x?5 m??v =0??????t?10s ???????? ???a?
?2
dv
?4?3t dt
??????dv?(4?3t)dt ????
3
v?4t?t2?c1
2
????t?0,v0?0 ,?c1?0
32t 2
dx3?4t?t2 ??? v?dt2
32
????? dx?(4t?t)dt
2
132
??? x?2t?t?c2
2
?v?4t???? t?0,x0?5 ,?c2?5 ? x?2t???t?10s?
2
13
t?5 2
v10?4?10?
3
?102?190m?s?12
1
x10?2?102??103?5?705m
2
3
1-11 ???????1 m ??????????? ?=2+3t?????????t??????(1) t?2 s???????????????(2)???????????45???????????
?? ??
d?d??9t2,???18t dtdt
(1)t?2s?? a??R??1?18?2?36m?s?2
an?R?2?1?(9?22)2?1296m?s?2
(2)??????????45????
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tan45??
2
a?
?1 an
? R??R? ??(9t)?18t
22
??????????(????????)????????
???? ???
1-1 ??r???r ?????
drdrdvdv?????? ?????????????dtdtdtdt??r???????????r?r2?r1??r?r2?r1?
??????
???1??r???????
?2?
drdrds
?v????????.
dtdtdt
dr
???????????. dt
????r?????????r?rr??
??
?drdrdr
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dtdtdt
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??????????? dt
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drdr
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dvdv?dv (3)?????????a??????a???????.
dtdtdt
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??
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dvdv?d?
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dtdtdt
dv
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1-2 ?????????x=x(t)?y=y(t)???????????????????
d2rdr?r?x?y?????v =??a?2??????????????????
dtdt
2
2
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dx??dy?
v=??????a=
dt???dt?
22
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22
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?drdx?dy??v??i?j
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dtdtdt
???????
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v?v?v??????
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2x
2y
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2
22
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????
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2
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1-3 ????xOy???????????
x=3t+5, y=
12
t+3t-4. 2
??t? s??x,y?m??(1)???t?????????????????(2)??t=1 s ???t?2s ???????????1????????(3)??t?0 s???t?4s?????????(4)??????????????t?4 s ???????(5)??t?0s ?t?4s ??????????(6)????????????????t?4s ???????(?????????????????????????????????????????????)??
?12??
???1? r?(3t?5)i?(t?3t?4)jm
2
(2)?t?1,t?2??????
???
r1?8i?0.5j m
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r2?11j?4jm ?????
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????????rr4?r012i?20j
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?t4?04
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dt
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(5)? v0?3i?3j,v4?3i?7j
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1-4 ?????h???????????????????S????1-4???????
v0(m2s?1)???????????????????????
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2
2
2
2l
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dlds?v0,v??? dtdt
vdsldll???v0?0 dtsdtscos?
? v?
lv0(h2?s2)1/2v0
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ss
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a???2v0?v0
2
dtss
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hv0??
s2s3
s
1-5 ???x??????????????? a?2+6x?a????m?s?x???? m. ???x?0?????10m?s,??????????????? ?? ?a?
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2
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dvdvdxdv
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2
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12
v?2x?2x3?c 2
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1-6 ???????????????? a?4+3t m?s???????x?5 m??v =0??????t?10s ???????? ???a?
?2
3
?1
dv
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??????dv?(4?3t)dt ????
3
v?4t?t2?c1
2
????t?0,v0?0 ,?c1?0
32t 2
dx3
??? v??4t?t2
dt2
3
????? dx?(4t?t2)dt
2
1
??? x?2t2?t3?c2
2
?v?4t???? t?0,x0?5 ,?c2?5 ? x?2t2???t?10s?
13
t?5 2
v10?4?10?
3
?102?190m?s?12 1
x10?2?102??103?5?705m
2
3
1-7 ???????1 m ??????????? ?=2+3t?????????t??????(1) t?2 s???????????????(2)???????????45???????????
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d?d??9t2,???18t dtdt
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tan45??
2
a?
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2 92
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9.3 ????q????????????????????????(1)????????????????????????????????(?????????????????????)?(2)???????????????
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qq?(2
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9.6 ?????A?B??????????d?????S????????+q?-q?????????????f????f=
q24??0d
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9.7 ?l=15.0cmAB???????????=5.0x10-9Cm-1
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Q
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(1) ?????????dx?????dq?P??????dEP?
1?dx
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EP??dEP?
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(a?x)
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ll4??0
a?a?
2
2
1
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l
??0(4a2?l2)
2
?l?15cm???5.0?10?9C?m?1, a?12.5cm???
EP?6.74?102N?C?1??????
(2)
dEQ?
1?dx
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4??0x?d2
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l
? dEQy
1?dx?
4??0x2?d22
d2x?d
2
2
2
EQy??dEQy
l
d??24??2
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l2l?2
dx(x2?d22)
3
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2??0l?4d
2
22
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EQ?EQy?14.96?102N?C?1????y???
9.8 ?????R????????????????,????O????? ?: ?9.8?????dl?
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?P?????dEP???????? 4
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4??0r2?
lr2?
l2
2
l4
2
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cos?2??cos?1
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?
4??0r2?
l4
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l2
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ll)r2?42
2
2
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q 4l
qr
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ll)r2?42
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9.10(1)???q??????a???????????????????????????????(2)??????????????????????
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s
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q
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q
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9.11 ?????????6cm????10cm???????210?5Cm-3????5cm?8cm ,12cm ??????
5
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发表于 2019-9-13 23:46:11