µ±0 ¡Ü t £¼ 3sʱ£¬v > 0£¬ÇÒa > 0£¬Öʵã¼ÓËÙÔ˶¯¡£
´Ë¶Î·³ÌΪs1?x2?x1??10?12?3?2?32???10??18m µ±3 s< t ¡Ü 5sʱ£¬v £¼ 0£¬ÇÒa > 0£¬Öʵã¼õËÙÔ˶¯¡£ ´Ë¶Î·³ÌΪs2?x3?x2
???(?10?12?5?2?52)?(?10?12?3?2?32)?8m
ÔòÖʵãµÄ×Ü·³ÌΪ s?s1?s2?26m
9£®Ò»ÖʵãÑØ°ë¾¶R = 1mµÄÔ²¹ìµÀ×÷Ô²ÖÜÔ˶¯£¬Æä½ÇλÖÃÓëʱ¼äµÄ¹ØÏµÎª?ÔòÖʵãÔÚt?1sʱ£¬ÆäËٶȺͼÓËٶȵĴóС·Ö±ðΪ£º
A£®1m/s£¬1m/s2£» B£®1m/s£¬2m/s2£» C£®1m/s£¬
1£¬?t2?1£¨SI£©
22m/s2£» D£®2m/s£¬2m/s2¡£ £¨ C £©
d??t dt[֪ʶµã] ½ÇÁ¿ÓëÏßÁ¿¹ØÏµ¡£ [·ÖÎöÓë½â´ð] ½ÇËÙ¶È ?? ½Ç¼ÓËÙ¶È ??d?
?1rad/2sdt ËٶȵĴóСv??R?t?1?t
v2t2??t2 ÏßÏò¼ÓËÙ¶Èan?R1ÇÐÏò¼ÓËÙ¶Èa?dv?1m/s2 dt22an?a??t4?1
×ܼÓËÙ¶È a?Ôòµ±t=1sʱ£¬ÖʵãµÄËٶȺͼÓËٶȵĴóСΪ v?1m/s a?14?1?
10£®A¡¢BÁ½´¬¶¼ÒÔ2m/sµÄËÙÂÊÔÈËÙÐÐÊ»£¬ÇÒA´¬ÑØxÖáÕýÏòÔ˶¯£¬B´¬ÑØyÖáÕýÏòÔ˶¯¡£ÔòB´¬Ïà¶ÔÓÚA´¬µÄËÙ¶È£¨ÒÔm/sΪµ¥Î»£©Îª
A£®2i?2j£» B£®?2i?2j£»
C£®?2i?2j£» D£®2i?2j¡£ £¨ B £© [֪ʶµã] Ô˶¯Ïà¶ÔÐÔ£¬Ù¤ÀûÂÔËٶȱ任ʽ¡£
[·ÖÎöÓë½â´ð] È¡µØÃæÎª¾²Ö¹²Î¿¼ÏµSϵ£¬A´¬ÎªÔ˶¯²Î¿¼ÏµS¡¯Ïµ£¬B´¬ÎªÔ˶¯ÎïÌå¡£
2
Ôò¾ø¶ÔËÙ¶ÈΪ u = 2j Ç£Á¬ËÙ¶È v = 2i
¶øB´¬Ïà¶ÔÓÚA´¬µÄÏà¶ÔËÙ¶ÈΪ u??u?v?2j?2i ¼´ u???2i?2j
¶þ¡¢Ìî¿ÕÌâ
1£®Ò»ÖʵãÑØxÖá·½ÏòÔ˶¯£¬ÆäÔ˶¯·½³ÌΪx?10?9t Öʵãǰ2sµÄÎ»ÒÆÎª?r= ?2i m£» ÖʵãËٶȵıí´ïʽΪv?
£¬Ôò£º ?6t2?t3£¨SI£©
(?9?12t?3t3)i m/s£»
ÖʵãÑØxÖáµÄ×î´óËÙ¶ÈֵΪvmax= 3 m/s¡£ [֪ʶµã] µÚ¢ñÀàÎÊÌâ£¬Î»ÒÆµÄ¼ÆËã¡£
[·ÖÎöÓë½â´ð] ÒÑÖªÔ˶¯·½³ÌΪ x?10?9t?6t?t
t?0sµÄλʸ r0?10im
t?2sµÄλʸ r2?10?9?2?6?22?23i?8im Ôòǰ2sµÄÎ»ÒÆ ?r?r2?r0??2im ÖʵãµÄËÙ¶È v?23??dxi??9?12t?3t2im/s dt??ÖʵãµÄ¼ÓËٶȵĴóС a?µ±
dv?12?6t dtdv?12?6t?0ʱ£¬Öʵã¾ßÓÐ×î´óËÙ¶È£¬¼´t=2sʱ£¬×î´óËÙ¶ÈֵΪ dt vmax??9?12t?3t2??9?12?2?3?22?3m/s
2£®Ò»ÖʵãÔÚxOyÆ½ÃæÄÚÔ˶¯£¬ÆäÔ˶¯·½³ÌΪx?2t£¬y?19?2t£¨SI£©¡£Ôò
2x2 ÖʵãµÄ¹ì¼£·½³ÌΪ y? 19? £»
2 t?2sʱµÄλʸΪ r? 4i?11j m£» t?2sʱµÄËÙ¶ÈΪ v? 2i?8j m/s£» ǰ2sÄ򵀮½¾ùËÙ¶ÈΪ v? 2i?4j m/s¡£ [֪ʶµã] ¹ì¼£·½³ÌÓëÔ˶¯·½³Ì£¬¶þάµÚ¢ñÀàÎÊÌ⣬ʸÁ¿±í´ïʽ¡£ [·ÖÎöÓë½â´ð] ÒÑÖªÖʵãµÄÔ˶¯·½³ÌΪ
x?2t (1) y?19?2t2 (2) ÓÉʽ£¨1£©µÃt?x£¬´úÈëʽ£¨2£©¼´¿ÉµÃ 2x2ÖʵãµÄ¹ì¼£·½³Ì y?19?
2ÖʵãµÄλʸΪ r?2ti?19?2t2j
µ±t=2sʱ£¬ÖʵãµÄλʸΪ r?2?2i?19?2?22j??4i?11j?m ÖʵãµÄËÙ¶ÈΪ v?µ±t=2sʱ£¬ÖʵãµÄËÙ¶ÈΪ
v?2i?4?2j??2i?8j?m/s ÖʵãÔÚǰ2sÄ򵀮½¾ùËÙ¶ÈΪ v?????dr?2i?4tj dt?rr2?r0? ?t2 ???2?2i??19?2?2?2 ??2i?4j?m/s
?1?2?j?19j??
?23£®Ò»ÖʵãÑØxÖáÕý·½ÏòÔ˶¯£¬ÆäËÙ¶ÈΪv?8?3tm/s£¬µ±t?8sʱ£¬ÖʵãλÓÚÔµã×ó²à52m
´¦£¬ÔòÆäÔ˶¯·½³ÌΪx?t3ÇÒ¿ÉÖªµ±t?0ʱ£¬ÔµãµÄ³õʼλÖÃΪx0? -628 m£¬?8t?628m£»
³õËÙ¶ÈΪv0= 8 m/s¡£ [֪ʶµã] µÚ¢òÀàÎÊÌ⣬³õʼÌõ¼þ¡£ [·ÖÎöÓë½â´ð] һάÖʵãÔ˶¯ v?dx?8?3t2 £¨1£© dt·ÖÀë±äÁ¿ dx?8?3tdt »ý·Ö£¬ÇÒ×¢Òât?8sʱ£¬x??52m£¬¼´
3?2??x?52dx???8?3t?
t283Ôò x?52?8t?t?8?8?8 ¼´Ô˶¯·½³ÌΪ x?t?8t?628 £¨2£© ½«t?0´úÈëʽ£¨2£©£¬ÔòÖʵãµÄ³õʼλÖÃΪ x0??628m ½«t?0´úÈëʽ£¨1£©£¬ÔòÖʵãµÄ³õËÙ¶ÈΪ v0?8m/s
34£®ÔÚÖʵãÇúÏßÔ˶¯ÖУ¬ÇÐÏò¼ÓËÙ¶Èa¦ÓÊÇ·´Ó³ÖʵãÔ˶¯ËÙ¶È ´óС ±ä»¯µÄÎïÀíÁ¿£»¶ø·¨Ïò¼ÓËÙ¶ÈanÊÇ·´Ó³ÖʵãÔ˶¯ËÙ¶È ·½Ïò ±ä»¯µÄÎïÀíÁ¿¡£
Ò»ÖʵãÔÚxOyÆ½ÃæÄÚ×÷Å×ÎïÔ˶¯£¬Èçͼ1-4(a)Ëùʾ£¬Èô²»¼Æ¿ÕÆø×èÁ¦£¬ÊÔÔÚͼÉϱê³öP¡¢QÁ½µãµÄÇÐÏò¼ÓËÙ¶Èa¦ÓºÍ·¨Ïò¼ÓËÙ¶Èan¡£
yPPv0Oͼ1-4(a)
Qv0a=nganQa?
x
g ͼ1-4(b)
[֪ʶµã] ÇÐÏò¡¢·¨Ïò¼ÓËÙ¶È¡£
[·ÖÎöÓë½â´ð] ²»¼Æ¿ÕÆø×èÁ¦£¬Öʵã×÷Å×ÌåÔ˶¯Ê±£¬Ö»Êܵ½ÊúÖ±ÏòϵÄÖØÁ¦×÷Ó㬼´¼ÓËÙ¶ÈʼÖÕÏòÏÂÇÒ´óÐ¡ÎªÖØÁ¦¼ÓËÙ¶Èg£¬Òò´Ë×î¸ßµãPÖ»Óз¨Ïò¼ÓËÙ¶Èan?g£¬ÔÚQµã¼ÈÓÐÇÐÏò¼ÓËÙ¶Èa¦Ó£¬ÓÖÓз¨Ïò¼ÓËÙ¶Èan£¬·½ÏòÈçͼ1-4£¨b£©Ëùʾ¡£
5£®Èçͼ1-5(a)Ëùʾ£¬Ò»ÅÚµ¯×÷Å×ÌåÔ˶¯£¬ÔÚ¹ìµÀµÄPµã´¦£¬ÆäËÙÂÊΪv£¬ÇÒvÓëË®Æ½ÃæµÄ¼Ð½Ç
vdv? ?gsin? £»Pµã´¦µÄÇúÂʰ뾶?? Ϊ?£¬Ôò¸Ãʱ¿ÌÖʵãµÄ ¡£ dtgco?s[֪ʶµã] ×ÔÈ»×ø±êϵ£¬ a¦Ó¡¢an¡£
[·ÖÎöÓë½â´ð] Èçͼ1-5(b)Ëùʾ£¬Å×ÌåÔ˶¯µÄ¼ÓËٶȾÍÊÇÖØÁ¦¼ÓËÙ¶Èg£¬ËüµÄÇÐÏò·ÖÁ¿Îª
2a¦Ó?dv??gsin¦È£¬Ê½ÖиººÅ±íʾÇÐÏò¼ÓËÙ¶Èa¦ÓµÄ·½ÏòÓëËÙ¶Èv·½ÏòÏà·´¡£ dt·¨Ïò¼ÓËÙ¶È an?gco¦Ès?v2?
v2ÔòÓÉ´ËÖªPµã´¦µÄÇúÂʰ뾶Ϊ ??
gcos?yvv
PO?Pa??an ͼ1-5(a)
x
g ͼ1-5(b)
6£®Ò»ÖʵãÑØxÖá×÷Ö±ÏßÔ˶¯£¬Æäv¡« tÇúÏßÈçͼ1-6Ëùʾ¡£Èç¹ûtÔòt?4.5sʱ£¬ÖʵãµÄλÖÃΪx? m/s2¡£
[֪ʶµã] ͼÏßÔËÓ㬵ڢòÀàÎÊÌâ.
[·ÖÎöÓë½â´ð] ÔÚv£tͼÉÏ£¬ÇúÏßÈÎÒ»µãµÄбÂʱíÃ÷ÊǼÓËÙ¶È£¬¼´
2?0ʱ£¬ÖʵãλÓÚ×ø±êԵ㣬
961 m£¬ÖʵãËùÐеÄ·³ÌΪs? m£¬ÖʵãµÄ¼ÓËÙ¶ÈΪa? 2 412v(m/s)103142ͼ1-6 4.5t(s)dv a?tan¦È?
dtÏÞµÄΪ£s£¨¼´ÑØÏà·´·½ÏòÔ˶¯µÄ·³Ì£©¡£
ÒÀͼʾ¿ÉµÃ v?v0?a?t?t0? ÔÚ2s¡Üt£¼3sÄÚ£¬ a3?-1 ÔÚv£tͼÖÐÇúÏßËù°üΧµÄÃæ»ý±íʾµÄÊÇÖʵãÔ˶¯µÄ·³Ìs£¬´¦ÓÚµÚ¢ñÏóÏÞµÄΪ+s£¬´¦ÓÚµÚ¢ôÏó
?1?2??3m/s2£¬v30?2m/s
3?2ÔòËÙ¶È v?2?3?t?2???3t?8 ÖʵãµÄתÏòµã v??3t?8?0 t?8s 3Ôò´Ó0¡«
8sÄÚÖʵãµÄ·³ÌΪ s1?sABCD3?8??1???2113????m
2311m 3ÒÑÖªµ±t?0ʱ£¬x0?0£¬¶ø s1?xD?x0?´Ó
8s¡«4.5sÄÚ£¬ÖʵãµÄ·³ÌΪ s2?sDEFG3??98???1??2?3???117??????m
212ÓÉÓÚ
817m s¡«4.5sÄÚ£¬Öʵã×÷·´·½ÏòÔ˶¯£¬Ôò s2?xD?xG?3121711179???m 123124111761??m 31213Ôòt = 4.5sʱ£¬ÖʵãµÄλÖÃΪ xG?xD?´ËʱÖʵãµÄ·³ÌΪ s?s1?s2?ÓÉͼÇóбÂʵôËʱµÄ¼ÓËÙ¶ÈΪ a?
1?2m/s 0.5