Question

14£®Ò»Æû³µ£¨ÊÓΪÖʵ㣩ÒÔv₁=30m/sµÄËÙ¶ÈÐÐÊ»ÔÚ±ÊÖ±µÄ¸ßËÙ¹«Â·ÉÏ£¬Í¾ÖÐҪͨ¹ý³¤¶ÈL=1600mµÄËíµÀ£¬ÇÒͨ¹ýËíµÀʱ±ØÐëÒÔv₂=20m/sµÄËÙ¶ÈÐÐÊ»£¬¹ÊÆû³µÔÚ½øÈëËíµÀÇ°ÐèÌáÇ°¼õËÙ£¬Ê¹Æû³µ½øÈëËíµÀʱµÄËÙ¶ÈÇ¡ºÃΪv₂£¬µ±Æä´©¹ýËíµÀºóÓÖ¿ÉÒÔ¼ÓËÙ»Ö¸´µ½Ô­À´µÄËÙ¶Èv₁£®ÒÑÖªÆû³µÔÚ¼õËٺͼÓËÙ¹ý³ÌÖоù×öÔȱäËÙÖ±ÏßÔ˶¯£¬ÇÒ¼ÓËٶȴóС¾ùΪa=1m/s²£®
£¨1£©ÇóÆû³µ´Óv₁¿ªÊ¼¼õËÙµ½»Ö¸´µ½v₁ËùÓõÄʱ¼ät£®
£¨2£©ÎªÁËÃÖ²¹Æû³µ´©¹ýËíµÀ¹ý³ÌËùµ¢ÎóµÄʱ¼ä£¬Ë¾»úÔÚ¼ÓËÙµ½ËÙ¶Èv₃=33m/s£¨¸ßËÙ¹«Â·ÉÏÔÊÐíͨ¹ýµÄ×î´óËٶȣ©Ö®ºó»¹ÒªÔÈËÙÐÐʻʱ¼ät₀ÔÙÁ¢¼´¼õËÙ²¢»Ö¸´µ½Ô­À´µÄËÙ¶Èv₁£¬Çót₀µÄ´óС£®

Answer 1

·ÖÎö £¨1£©Õû¸öÔ˶¯¹ý³Ì·ÖΪÈý¸ö¹ý³Ì£¬¼´ÔȼõËÙÔ˶¯¡¢ÔÈËÙÔ˶¯¡¢ÔȼÓËÙÔ˶¯£¬·Ö±ðÇó³öÕâÈý¶ÎÔ˶¯µÄʱ¼ä¼´¿ÉÇó½â
£¨2£©¸ù¾ÝËٶȹ«Ê½Çó³öÕâ¶Î¹ý³ÌÔÈËÙÔ˶¯µÄʱ¼ä£¬´Ó¶øÇó³öµ¢ÎóµÄʱ¼ä£®

½â´ð ½â£º£¨1£©Éèͨ¹ýËíµÀÇ°¼õËÙ¹ý³ÌËùÐèʱ¼äΪt₁£¬Í¨¹ýËíµÀËùÓõÄʱ¼äΪt₂£¬Í¨¹ýËíµÀºó¼ÓËÙ¹ý³ÌËùÐèʱ¼äΪt₃£®ÔòÓУº
t₁=$\frac{{v}_{2}-{v}_{1}}{{a}_{1}}=\frac{20-30}{-1}=10$s£®
t₂=$\frac{L}{{v}_{2}}=\frac{1600}{20}=80$s
t₃=$\frac{{v}_{1}-{v}_{2}}{{a}_{2}}=\frac{30-20}{1}=10$s£®
¹²ÓÃʱ¼äΪ£ºt_×Ü=t₁+t₂+t₃=10+80+10=100s£®
£¨2£©¼õËÙͨ¹ýµÄλÒÆΪ£º${x}_{1}=\frac{{v}_{1}+{v}_{2}}{2}•{t}_{1}=\frac{30+20}{2}¡Á10=250$m
¼ÓËÙͨ¹ýµÄλÒÆΪ£º${x}_{2}=\frac{{v}_{1}+{v}_{2}}{2}•{t}_{3}=\frac{30+20}{2}¡Á10=250$m
ÒÔ30m/sͨ¹ýÈ«³ÌËùÐèʱ¼äΪ£º$t=\frac{{x}_{1}+{x}_{2}+L}{{v}_{1}}$=$\frac{250+1600+250}{30}=70$s
µ¢Îóʱ¼äΪ£º¡÷t=t_×Ü-t=100-70=30s
ËùÒÔÔÚ´©¹ýËíµÀµÄ¹ý³ÌÖÐÆû³µÉÙ×ßÁË£º¡÷s=v₁•¡÷t=30¡Á30=900m
ÔÚ´©¹ýËíµÀºó£¬¼ÓËÙµÄʱ¼ä£º${t}_{4}=\frac{{v}_{3}-{v}_{1}}{{a}_{2}}=\frac{33-30}{1}=3$s
¼õËÙµÄʱ¼ä£ºt₅=$\frac{{v}_{1}-{v}_{3}}{{a}_{1}}=\frac{30-33}{-1}=3$s
¼ÓËÙͨ¹ýµÄλÒÆΪ£º${x}_{4}=\frac{{v}_{1}+{v}_{3}}{2}•{t}_{4}=\frac{30+33}{2}¡Á3=94.5$m
¼õËÙͨ¹ýµÄλÒÆΪ£º${x}_{5}=\frac{{v}_{1}+{v}_{3}}{2}•{t}_{5}=\frac{30+33}{2}¡Á3=94.5$m
ÕâÁ½¶Îʱ¼äÄÚ±ÈÕý³£ÐÐÊ»¶à×ߣº¡÷s₁=x₄+x₅-v₁£¨t₄+t₅£©=94.5+94.5-30¡Á6=9m
Æû³µÔÚʱ¼ät₀ÄÚÐèÒª¶à×ߣºL=¡÷s-¡÷s₁=900-9=891m
ËùÒÔ£º${t}_{0}=\frac{L}{{v}_{3}-{v}_{1}}=\frac{891}{33-30}=297$s
´ð£º£¨1£©Æû³µ´Óv₁¿ªÊ¼¼õËÙµ½»Ö¸´µ½v₁ËùÓõÄʱ¼äÊÇ100s£®
£¨2£©ÎªÁËÃÖ²¹Æû³µ´©¹ýËíµÀ¹ý³ÌËùµ¢ÎóµÄʱ¼ä£¬Ë¾»úÔÚ¼ÓËÙµ½ËÙ¶Èv₃=33m/s£¨¸ßËÙ¹«Â·ÉÏÔÊÐíͨ¹ýµÄ×î´óËٶȣ©Ö®ºó»¹ÒªÔÈËÙÐÐʻʱ¼ät₀ÔÙÁ¢¼´¼õËÙ²¢»Ö¸´µ½Ô­À´µÄËÙ¶Èv₁£¬t₀µÄ´óСÊÇ297s£®

µãÆÀ ±¾ÌâÖ÷Òª¿¼²éÁËÔȱäËÙÖ±ÏßÔ˶¯ËÙ¶Èʱ¼ä¹«Ê½µÄÖ±½ÓÓ¦Ó㬹ý³ÌËäÈ»±È½Ï¶à£¬µ«ÄѶȲ»´ó£¬¹Ø¼üÊÇ·ÖÎöºÃ¹ý³Ì£®