Question

6£®Ä³È˼ÝʻһÁ¾Æû³µ¼×ÕýÔÚƽֱµÄ¹«Â·ÒÔijһËÙ¶ÈÔÈËÙÔ˶¯£¬Í»È»·¢ÏÖÇ°·½50m´¦Í£×ÅÒ»Á¾ÒÒ³µ£¬Á¢¼´É²³µ£¬É²³µºó×öÔȼõËÙÖ±ÏßÔ˶¯£®ÒÑÖª¸Ã³µÉ²³µºóµÚ1¸ö2sÄÚµÄλÒÆÊÇ24m£¬µÚ4¸ö2sÄÚµÄλÒÆÊÇ1m£®ÔòÏÂÁÐ˵·¨ÕýÈ·µÄÊÇ£¨¡¡¡¡£©

• A£® Æû³µ¼×ɲ³µºó×öÔȼõËÙÖ±ÏßÔ˶¯µÄ¼ÓËٶȴóСΪ$\frac{23}{12}$m/s²
• B£® Æû³µ¼×ɲ³µºó×öÔȼõËÙÖ±ÏßÔ˶¯µÄ¼ÓËٶȴóСΪ2m/s²
• C£® Æû³µ¼×ɲ³µºóֹͣǰ£¬¿ÉÄÜײÉÏÒÒ³µ
• D£® Æû³µ¼×ɲ³µÇ°µÄËÙ¶ÈΪ14m/s

Answer 1

·ÖÎö ¸ù¾ÝÔȱäËÙÖ±ÏßÔ˶¯µÄÍÆÂÛ£¬ÔËÓÃÁ¬ÐøÏàµÈʱ¼äÄÚµÄλÒÆÖ®²îÊÇÒ»ºãÁ¿£¬Çó³ö¼ÓËٶȣ¬½áºÏλÒÆʱ¼ä¹«Ê½Çó³ö³õËٶȣ¬ÅжÏËٶȼõΪÁãµÄʱ¼ä£¬ÅжϳöÎïÌåÔÚ8sÇ°ÒѾ­Í£Ö¹£¬ÔÙ½áºÏÔ˶¯Ñ§¹«Ê½Çó³ö³õËٶȺͼÓËٶȣ®¸ù¾ÝËÙ¶ÈλÒƹ«Ê½Çó³öÆû³µÉ²³µµ½Í£Ö¹µÄ¾àÀ룬Åжϼ׳µÊÇ·ñײÉÏÒÒ³µ£®

½â´ð ½â£ºABD¡¢¼ÙÉè8sÄÚÒ»Ö±×öÔȼõËÙÖ±ÏßÔ˶¯£¬¸ù¾Ý${x}_{4}^{\;}-{x}_{1}^{\;}=3a{T}_{\;}^{2}$µÃ£ºa=$\frac{{x}_{4}^{\;}-{x}_{1}^{\;}}{3{T}_{\;}^{2}}$=$\frac{1-24}{3¡Á4}$=-$\frac{23}{12}$$m/{s}_{\;}^{2}$£¬
¸ù¾Ý${x}_{1}^{\;}={v}_{0}^{\;}{t}_{1}^{\;}+\frac{1}{2}a{t}_{1}^{2}$µÃ³õËÙ¶ÈΪ£ºv₀=$\frac{24+\frac{1}{2}¡Á\frac{23}{12}¡Á{2}_{\;}^{2}}{2}$m/s¡Ö14m/s£¬
ËٶȼõΪÁãµÄʱ¼äΪ£ºt=$\frac{0-{v}_{0}^{\;}}{a}$=$\frac{0-14}{-\frac{23}{12}}$s=7.3s£¬¿ÉÖªÆû³µÔÚ8sÇ°ËٶȼõΪÁ㣮
ÉèÆû³µµÄ¼ÓËÙ¶ÈΪa£¬¸ù¾Ý${x}_{1}^{\;}={v}_{0}^{\;}{t}_{1}^{\;}+\frac{1}{2}a{t}_{1}^{2}$µÃ£º24=2v₀+2a£¬Æû³µËٶȼõΪÁãµÄʱ¼äΪ£ºt₀=$\frac{0-{v}_{0}^{\;}}{a}$=$\frac{-{v}_{0}^{\;}}{a}$£¬
²ÉÓÃÄæÏò˼ά£¬×îºó2sÄÚµÄλÒÆΪ£ºx¡ä=$\frac{1}{2}$£¨-a£©$£¨\frac{{v}_{0}^{\;}}{-a}-6£©_{\;}^{2}$=1m£¬ÁªÁ¢½âµÃa=-2m/s²£¬³õËÙ¶Èv₀=14m/s£¬¹ÊBDÕýÈ·£¬A´íÎó£®
C¡¢Æû³µÉ²³µµ½Í£Ö¹µÄ¾àÀëx₀=$\frac{0-{v}_{0}^{2}}{2a}$=$\frac{0-1{4}_{\;}^{2}}{2¡Á£¨-2£©}$m=49m£¼50m£¬¿ÉÖª¼×²»ÄÜײÉÏÒÒ³µ£¬¹ÊC´íÎó£®
¹ÊÑ¡£ºBD£®

µãÆÀ ½â¾ö±¾ÌâµÄ¹Ø¼üÕÆÎÕÔȱäËÙÖ±ÏßÔ˶¯µÄÔ˶¯Ñ§¹«Ê½ºÍÍÆÂÛ£¬²¢ÄÜÁé»îÔËÓã¬×¢ÒâÎïÌåÔÚ8sÇ°ÒѾ­Í£Ö¹£¬ËùÒÔͨ¹ýÁ¬ÐøÏàµÈʱ¼äÄÚµÄλÒÆÖ®²îÊÇÒ»ºãÁ¿Çó³öµÄ¼ÓËÙ¶ÈÊÇ´íÎóµÄ£®