ϰÌ⾫½â½âÌâ·½·¨ÓëÀýÌâ·ÖÎö
Ò»¡¢ÒÑÖªÔ˶¯·½³Ì£¨Î»ÖÃʸÁ¿£©£¬¼ÆËãÎ»ÒÆ¡¢ËٶȺͼÓËÙ¶È¡£
¼ÆË㣨˲ʱ£©ËٶȺͼÓËÙ¶ÈÒ»°ãÓÃÇ󵼵ķ½·¨£ºÎ»ÖÃʸÁ¿£¨Ô˶¯·½³Ì£©¶Ôʱ¼äÇóµ¼¼´ÎªËÙ¶È£¬ËٶȶÔʱ¼äÇóµ¼¾ÍÊǼÓËÙ¶È¡£¼ÆËãÎ»ÒÆ¡¢Æ½¾ùËÙ¶È¡¢Æ½¾ù¼ÓËÙ¶È¿ÉÏÈÓÉʼĩʱ¿ÌÈ·¶¨Ê¼Ä©Î»Öã¬ÔÙÓɶ¨Ò弯Ëã¡£
Àý1 Ò»ÖʵãÔÚÆ½ÃæÉÏÔ˶¯£¬ÒÑÖªÖʵãλÖÃʸÁ¿µÄ±í´ïʽΪ
r?at2i?bt2j £¨ÆäÖÐa¡¢bΪ³£Á¿£©£¬
Ôò¸ÃÖʵã×÷ºÎÖÖÐÎʽµÄÔ˶¯£¿
½â ÓÉÖʵãµÄλÖÃʸÁ¿ r?at2i?bt2j
2??x?atµÃÔ˶¯·½³Ì ? 2??y?bt¹ìµÀ·½³Ì
xab?£¬ y?x ybaÖʵãµÄËÙ¶È v?dr?2ati?2btj dtdv?2ai?2bj dtbx¡£ aÖʵãµÄ¼ÓËÙ¶È a?ÖʵãµÄ¼ÓËÙ¶ÈΪ·ÇÁãºãÁ¿£¬¹Ê¸ÃÖʵãÔÚxyÆ½ÃæÄÚ×÷ÔȱäËÙÖ±ÏßÔ˶¯£¬Æä¹ìµÀ·½³ÌΪy?3
Àý2 ijÖʵãµÄÔ˶¯·½³ÌΪ x =2t¨C7t+3£¨SI£©£¬Ôò¸ÃÖʵã×÷ºÎÖÖÐÎʽµÄÔ˶¯£¿²¢È·¶¨¼ÓËٶȵķ½Ïò¡£ ½â ÓÉÖʵãµÄÔ˶¯·½³Ì x =2t¨C7t+3 µÃÖʵãµÄËÙ¶È v?ÖʵãµÄ¼ÓËÙ¶È a?3
dx?2?21t2 dtdv??42t dtÖʵãµÄ¼ÓËÙ¶ÈΪʱ¼äµÄº¯Êý£¬¹Ê¸ÃÖʵã×÷±ä¼ÓËÙÖ±ÏßÔ˶¯£»¼ÓËÙ¶ÈΪ¸º£¬ËµÃ÷¼ÓËÙ¶È·½ÏòÑØxÖḺ·½Ïò¡£ Àý3 Ò»ÖʵãÑØxÖá×÷Ö±ÏßÔ˶¯£¬tʱ¿ÌµÄ×ø±êΪx =5t¨C 3t (SI)¡£ÊÔÇó£º
2
3
£¨1£©ÔÚµÚ2ÃëÄ򵀮½¾ùËÙ¶È£» £¨2£©µÚ2ÃëÄ©µÄ˲ʱËÙ¶È£» £¨3£©µÚ2ÃëÄ©µÄ¼ÓËÙ¶È¡£ ½â £¨1£©ÓÉÆ½¾ùËٶȵ͍Ò壺
v??x/?t
(5?22?3?23)?(5?12?3?13)???6m/s
2?1£¨2£©Óɶ¨Òå v?dx/dt?10t?9t2
t?2sʱ£¬ÓÐ v2??16m/s
£¨3£©Óɶ¨Òå a?dv/dt?10?18t
t?2sʱ£¬ÓÐ a2??26m/s2
Àý4 ÔÚÀë´¬¸ß¶ÈΪhµÄ°¶±ß£¬½Ê³µÒԺ㶨µÄËÙÂÊv0ÊÕÉþ£¨ÉþÔ³¤l0£©£¬Ê¹´¬¿¿°¶£¬Èçͼ1¡ª1Ëùʾ£¬ÊÔÃèÊö´¬µÄÔ˶¯¡£
½â ½¨Á¢ÈçÍ¼×ø±êϵ£¬ÏÔÈ»´¬
l?l0?v0t
v0hÔÚxÖáÉÏ×÷Ö±ÏßÔ˶¯¡£tʱ¿ÌÉþ³¤Îª
l´¬µÄÔ˶¯·½³ÌΪ
x?(l0?v0t)2?h2 ËÙ¶ÈΪ v?(l0?v0t)v0dx??
22dt(l0?v0t)?hoxxͼ1¡ª1
·½ÏòÑØxÖḺÏò¡£
v0h2dv¼ÓËÙ¶ÈΪ a???dt(l0?v0t)2?h22??32?v0h2 ?3x2·½ÏòÑØxÖḺÏò¡£
¿É¼û£¬´¬×÷¼ÓËÙÖ±ÏßÔ˶¯£¬Àë°¶Ô½½ü£¬xԽС£¬aÔ½´ó¡£
Àý5 ÒÑÖªÖʵãµÄÔ˶¯·½³Ìx=2t£¬y=4¨Ct£¨SI£©¡£ÊÔÇóÈÎһʱ¿ÌÖʵãµÄËÙ¶È¡¢ÇÐÏò¼ÓËÙ¶È¡¢·¨Ïò¼ÓËÙ¶È¡¢×ܼÓËٶȵĴóС¡£
2
½â ÓÉÔ˶¯·½³Ì¿ÉÇóµÃÖʵãËٶȵÄx¡¢y·ÖÁ¿
vx?dxdy?2, vy???2t dtdt22ËÙ¶È´óСΪ v?vx?vy?21?t2
ͬÀí£ºax?dvydvx2
??2 m/s ?0£¬ ay?dtdt2
ËùÒÔ¼ÓËÙ¶È´óСΪ a?ay??2 m/s ÇÐÏò¼ÓËÙ¶È£ºat?dv2t ?2dt1?t2·¨Ïò¼ÓËÙ¶È£ºan?a2?at?21?t2
¶þ¡¢ÒÑÖª¼ÓËٶȼ°³õʼÌõ¼þ£¬¼ÆËãËٶȺÍÔ˶¯·½³Ì¡£
´ËÀàÎÊÌâÊÇǰһÀàÎÊÌâµÄÄæ¹ý³Ì£¬¼ÓËٶȶÔʱ¼äµÄ»ý·Ö¼´ÎªËÙ¶È£¬ËٶȶÔʱ¼äµÄ»ý·Ö¾ÍÊÇÔ˶¯·½³Ì¡£½â¾ö´ËÀàÎÊÌâʱӦעÒâÓɳõʼÌõ¼þÈ·¶¨»ý·ÖÉÏÏÂÏÞ¡£
Àý6 Ò»ÖʵãÑØxÖáÔ˶¯£¬Æä¼ÓËÙ¶ÈaÓëλÖÃ×ø±êµÄ¹ØÏµÎª a=3+6x£¨SI£©¡£Èç¹ûÖʵãÔÚԵ㴦µÄËÙ¶ÈΪÁ㣬ÊÔÇóÆäÔÚÈÎÒâλÖô¦µÄËÙ¶È¡£
½â ÉèÖʵãÔÚÈÎÒâλÖÃx´¦µÄËÙ¶ÈΪv£¬Ôò a?2
dvdvdxdv?3?6x2 ???vdtdxdtdx·ÖÀë±äÁ¿£¬Á½±ß»ý·Ö£º
?v0vdv??(3?6x2)dx
0xµÃ v?6x?4x3
Àý7 Ò»ËÒÕýÔÚÐÐÊ»µÄÆû´¬£¬µ±¹Ø±Õ·¢¶¯»úºó£¬ÑØÒ»Ö±ÏßÔ˶¯£¬¼ÓËÙ¶ÈÓë´¬ËÙµÄÆ½·½³ÉÕý±ÈÇÒ·´Ïò£¬¼´a??kv2£¬ÆäÖг£Á¿k>0¡£Èô¹Ø±Õ·¢¶¯»úʱÆû´¬µÄËÙ¶ÈΪv0£¬Çó£º
£¨1£©¹Ø±Õ·¢¶¯»úºótʱ¿ÌµÄÆû´¬ËÙ¶È£»
£¨2£©¹Ø±Õ·¢¶¯»úºóµÄtʱ¼äÄÚ£¬Æû´¬ÐÐÊ»µÄ¾àÀë¡£
½â ÒÔÆû´¬ÎªÑо¿¶ÔÏó£¬ÓÉÓÚËü×ö¼õËÙÖ±ÏßÔ˶¯£¬ËùÒÔÈ¡Æû´¬Ô˶¯·½ÏòÎª×ø±êÖáxµÄÕý·½Ïò£¬×ø±êÔµãÑ¡ÔñÔڸչرշ¢¶¯»úµÄλÖô¦¡£
£¨1£©°´Ö±ÏßÔ˶¯µÄ¼ÓËٶȹ«Ê½ÓÐ a?ÓÉÌâÒâa??kv2£¬´úÈëÉÏʽ£¬ÓÐ ?kv2?·ÖÀë±äÁ¿ kdt??dv dtdv dtdv v2ÒÑÖªt=0ʱ£¬v?v0£¬²¢Éètʱ¿ÌµÄËÙ¶ÈΪv£¬¶ÔÉÏʽȡ¶¨»ý·Ö
k?dt???0v0tvdv v2¡à v?v0
kv0t?1dx dt£¨2£©ÓÉ v?ÓÐ
v0dx? dtkv0t?1·ÖÀë±äÁ¿£¬Á½±ßÈ¡¶¨»ý·Ö£¬ÓÐ
?x0dx??t0v0dt
kv0t?1