Question

7£®A¡¢BÁ½Æû³µÏà¾à14m£¬ÑØͬһֱÏßͬÏòÔ˶¯£¬A³µÔÚºó£¬B³µÔÚÇ°£®B³µÒÔ5m/sµÄËÙ¶ÈÔÈËÙ£¬A³µ´Ó¾²Ö¹¿ªÊ¼ÒÔ2m/s²µÄ¼ÓËٶȼÓËÙ£®Çó£º
£¨1£©ºÎʱÁ½³µÏà¾à×îÔ¶£¿×îÔ¶¾àÀëΪ¶àÉÙ£¿
£¨2£©¾­¶à³¤Ê±¼äÁ½³µÏàÓö£¿
£¨3£©ÈôA¡¢BÁ½Á¾³µÏà¾à2m£¬ÑØͬһֱÏßͬÏòÔ˶¯£¬B³µÔÚÇ°×ö³õËÙ¶ÈΪÁ㣬¼ÓËÙ¶ÈΪa₁ÊÇÔȼÓËÙÖ±ÏßÔ˶¯£¬A³µÔÚºóÃæ×ö³õËÙ¶ÈΪ2m/s£¬¼ÓËÙ¶Èa₂µÄÔȼÓËÙÖ±ÏßÔ˶¯£¬ÌÖÂÛa₁Óëa₁Âú×ãʲôÌõ¼þʱÁ½³µÏàÓöÒ»´Î£¿

Answer 1

·ÖÎö £¨1£©µ±Á½³µËÙ¶ÈÏàµÈʱ£¬Ïà¾à×îÔ¶£¬½áºÏËÙ¶Èʱ¼ä¹«Ê½Çó³öËÙ¶ÈÏàµÈ¾­ÀúµÄʱ¼ä£¬½áºÏλÒƹ«Ê½Çó³ö×îÔ¶¾àÀ룮
£¨2£©¸ù¾ÝλÒƹØϵ£¬½áºÏÔ˶¯Ñ§¹«Ê½Çó³ö×·¼°µÄʱ¼ä£®
£¨3£©¸ù¾ÝλÒÆʱ¼ä¹«Ê½µÃ³öÁ½³µÎ»ÒÆÏàµÈµÄ±í´ïʽ£¬½áºÏÅбðʽ½øÐÐÅжϣ®

½â´ð ½â£º£¨1£©Éèt₁ʱÁ½³µËÙ¶ÈÏàµÈ£¬´ËʱÁ½³µÏà¾à×îÔ¶£¬ÓУºv_B=at₁
t₁=$\frac{{v}_{B}}{a}=\frac{5}{2}s=2.5s$£¬
Ôò×îÔ¶¾àÀëΪ£º¡÷x=x₀+v_Bt₁-$\frac{1}{2}$at₁²=$14+5¡Á2.5-\frac{1}{2}¡Á2¡Á2£®{5}^{2}$m=20.25m
£¨2£©Éèt₂ʱÁ½³µÏàÓöÓУº
ÓУºx_A=x_B+x₀
¼´£º$\frac{1}{2}$at₂²=v_Bt₂+x₀
´úÈëÊý¾Ý½âµÃ£ºt₂=7s
£¨3£©1¡¢Á½³µµÄ¼ÓËÙ¶ÈÏàµÈʱ£®
Òòºó³µ£¨A³µ£©¾ßÓгõËٶȣ¬Ç°³µ£¨B³µ£©ÉϵÄΪÁ㣬Á½³µ»áÏàÓöÒ»´Î£®
2¡¢µ±Á½³µµÄ¼ÓËٶȲ»ÏàµÈʱ£®
¶ÔA£ºx₁=v₀t+$\frac{1}{2}$a₂t²
¶ÔB£ºx₂=$\frac{1}{2}$a₁t²
ÏàÓö£ºx₁=x₂+x₀
¼´£ºv₀t+$\frac{1}{2}$a₂t²=$\frac{1}{2}$a₁t²+x₀
$\frac{1}{2}$£¨a₂-a₁£©t²+v₀t-x₀=0
´úÈëÊýÖµ£º$\frac{1}{2}$£¨a₂-a₁£©t²+2t-2=0
µ±4+4£¨a₂-a₁£©=0ʱ£¬¸Ã·½³ÌÖ»ÓÐÒ»½â£¬¼´ÏàÓöÒ»´Î£¬¿ÉÖªa₂-a₁=-1m/s²Ê±£¬ÏàÓöÒ»´Î£®
´ð£º£¨1£©¾­¹ý2.5sʱÏà¾à×îÔ¶£¬×îÔ¶¾àÀëΪ20.25m£®
£¨2£©¾­¹ý7sʱ¼äÏàÓö£®
£¨3£©µ±a₂-a₁=-1m/s²Ê±»òa₂=a₁£¬ÏàÓöÒ»´Î£®

µãÆÀ ±¾Ì⿼²éÁËÔ˶¯Ñ§ÖеÄ×·¼°ÎÊÌ⣬¹Ø¼üץסλÒƹØϵ£¬½áºÏÔ˶¯Ñ§¹«Ê½Áé»îÇó½â£¬ÖªµÀËÙ¶ÈÏàµÈʱÏà¾à×îÔ¶£®