Question

1£®ÈçͼËùʾ£¬Ä³Í¬Ñ§ÔÚ×ö¡°Ñо¿ÔȱäËÙÖ±ÏßÔ˶¯¡±ÊµÑéÖУ¬ÓÉ´òµã¼ÆʱÆ÷µÃµ½±íʾС³µÔ˶¯¹ý³ÌµÄÒ»ÌõÇåÎúÖ½´ø£¬Ö½´øÉÏÁ½ÏàÁÚ¼ÆÊýµãµÄʱ¼ä¼ä¸ôΪT=0.10s£¬ÆäÖÐx₁=7.05cm£¬x₂=7.68cm£¬x₃=8.31cm£¬x₄=8.95cm£¬x₅=9.61cm£¬x₆=10.25cm£¬£¨¼ÆËã½á¹û±£ÁôÁ½Î»ÓÐЧÊý×Ö£©
£¨1£©Aµã´¦Ë²Ê±ËٶȵĴóСÊÇ0.86m/s£»
£¨2£©Ð¡³µÔ˶¯µÄ¼ÓËٶȼÆËã±í´ïʽΪa=$\frac{{x}_{6}+{x}_{5}+{x}_{4}-{x}_{3}-{x}_{2}-{x}_{1}}{9{T}^{2}}$£¬¼ÓËٶȵĴóСÊÇ0.64m/s²£®

Answer 1

·ÖÎö Ö½´øʵÑéÖУ¬ÈôÖ½´øÔȱäËÙÖ±ÏßÔ˶¯£¬²âµÃÖ½´øÉϵĵã¼ä¾à£¬ÀûÓÃÔȱäËÙÖ±ÏßÔ˶¯µÄÍÆÂÛ£¬¿É¼ÆËã³ö´ò³öijµãʱֽ´øÔ˶¯µÄ˲ʱËٶȺͼÓËÙ¶È

½â´ð ½â£ºx₁=7.05cm=0.0705m£¬x₂=7.68cm=0.0768m£¬x₃=8.31cm=0.0831m£¬x₄=8.95cm=0.0895m£¬x₅=9.61cm=0.0961m£¬x₆=10.25cm=0.1025m
ÀûÓÃÔȱäËÙÖ±ÏßÔ˶¯µÄÍÆÂ۵ãº
v_D=$\frac{{x}_{3}+{x}_{4}}{2T}=\frac{0.0833+0.0895}{0.2}$=0.86m/s£®
ÓÉÓÚÏàÁڵļÆÊýµã¼äµÄλÒÆÖ®²î²»µÈ£¬¹Ê²ÉÓÃÖð²î·¨Çó½â¼ÓËٶȣ®
¸ù¾ÝÔȱäËÙÖ±ÏßÔ˶¯µÄÍÆÂÛ¹«Ê½¡÷x=aT²¿ÉÒÔÇó³ö¼ÓËٶȵĴóС£¬
µÃ£ºx₄-x₁=3a₁T² 
x₅-x₂=3a₂T² 
 x₆-x₃=3a₃T² 
ΪÁ˸ü¼Ó׼ȷµÄÇó½â¼ÓËٶȣ¬ÎÒÃǶÔÈý¸ö¼ÓËÙ¶Èȡƽ¾ùÖµ£º
µÃ£ºa=$\frac{1}{3}$£¨a₁+a₂+a₃£©
С³µÔ˶¯µÄ¼ÓËٶȼÆËã±í´ïʽΪa=$\frac{{x}_{6}+{x}_{5}+{x}_{4}-{x}_{3}-{x}_{2}-{x}_{1}}{9{T}^{2}}$
´úÈëÊý¾ÝµÃa=0.64m/s²£®
¹Ê´ð°¸Îª£º0.86£¬a=$\frac{{x}_{6}+{x}_{5}+{x}_{4}-{x}_{3}-{x}_{2}-{x}_{1}}{9{T}^{2}}$£¬0.64

µãÆÀ ̽¾¿¼ÓËÙÓëÁ¦µÄ¹ØϵʵÑéʱ£¬ÒªÆ½ºâĦ²ÁÁ¦¡¢Ó¦¸ù¾ÝÖ½´øÇó³öС³µµÄ¼ÓËٶȣ¬ÕÆÎÕʵÑéµÄʵÑé×¢ÒâÊÂÏîÊÇÕýÈ·½âÌâµÄ¹Ø¼ü£¬×¢ÒⵥλµÄ»»ËãºÍÓÐЧÊý×ֵı£Áô£¬Äܹ»ÔËÓÃÖð²î·¨Çó½â¼ÓËÙ¶È