物体运动规律为S=3t^2,在t=3时的瞬时速度是
\u82e5\u4e00\u7269\u4f53\u8fd0\u52a8\u65b9\u7a0b\u5982\u4e0b S=3t^2+2 (0\u2264t\uff1c3) \u2460 S= 29+3(t-3)^2 (t\u22653) \u2461 \u5219t=1\u548ct=3\u65f6\u7684\u77ac\u65f6\u901f\u5ea6v=S\u2018\uff08t\uff09=6t (0\u2264t\uff1c3)
v=S\u2018\uff08t\uff09=6t-18 (t\u22653)
t=1\u65f6\uff0cv=S\u2019\uff081\uff09=6
t=3\u65f6\uff0cv=S\u2018\uff083\uff09=6\u00d73-18=0
dui\u5bf9s\u6c42\u5bfc\u6570 s\u2032 =6t v=6t 6*3=18
方法一:S=3t^2,求导得:V=3*2t=6t,加速度为6,3秒时速度是18m/s方法二:S=0.5at2=3t2,所以,0.5a=3,a=6,vt=at=6*3=18m/s
两种方法,
1、v=ds/dt=6t
2、对比s=v0t+0.5at^2,可知v0=0,a=6。所以v=6t
绛旓細绛旀锛氳В鏋愶細(6锛3螖t)锛6锛屾墍浠锛岀墿浣撳湪t锛1鏃剁殑鐬椂閫熷害鏄6锛庢彁绀猴細姹傛洸绾縴锛漻2锛1涓婃煇涓鐐瑰垏绾跨殑鏂滅巼鏈変袱绉嶆柟娉曪細涓銆佄旀硶锛氬洜涓哄垏绾挎柟绋嬩笌鏇茬嚎y锛漻2锛1鏈変竴涓氦鐐癸紝鎵浠ュ畠浠粍鎴愮殑鏂圭▼缁勪粎鏈変竴缁勫疄鏁拌В锛涗簩銆佸鏁版硶锛
绛旓細v锛坱锛=3t^2 褰搕=2 v=12m/s
绛旓細s(t)=3t*2+t+4 鈻硈/鈻硉=[s锛4+鈻硉锛-s锛4锛塢/鈻硉 =[3锛4+鈻硉锛*2+鈻硉+4-56-锛3x4*2+4+4锛塢鈻硉 =[48+24鈻硉+3x鈻硉*2+鈻硉+4-56]=3鈻硉+25
绛旓細鏍规嵁瀵兼暟鐨勭墿鐞嗘剰涔夛紝鐬椂閫熷害涓 s'(t)=(t^3)'=3t^2 鎵浠ワ紝t=2s鏃剁殑鐬椂閫熷害涓 s'(2)=3脳2^2=12(m/s)
绛旓細姹傚嚭S锛坱锛夌殑瀵兼暟涓篠'锛坱锛=6t+2锛鎵浠ヨ鐗╀綋鍦t=2鏃跺埢鐨勭灛鏃堕熷害鏄疭'锛2锛=14
绛旓細棰濃︹﹁繖搴旇娑夊強鍒伴珮浜岀殑瀵兼暟锛屼笉鐭ラ亾浣犳湁娌℃湁瀛﹁繃銆傝繕鏈夊簲璇鏄痵锛3t²锛媡 鍚 涓嶇劧鐨勮瘽娌℃湁绛旀 鍏堟眰瀵糞鈥=6t +1 褰搕=2 6脳2+1=13
绛旓細杩欎釜鏄纭殑銆傛病鏈変笉瀵广傞偅涓В閲婄函绮硅儭璇村叓閬擄紝濡傛灉鏄建杩规柟绋媦=4/3x纭疄鏄笉鑳界‘瀹氥備絾鏄鐩腑鏄繍鍔鏂圭▼锛岄熷害鏄畬鍏ㄧ‘瀹氱殑銆倂=ds/dt.鎴戝啀寮鸿皟涓閬嶏細鍘熷懡棰樻槸瀹屽叏姝g‘鐨勩
绛旓細鏍规嵁瀵兼暟鐨勭墿鐞嗘剰涔夛紝鐬椂閫熷害涓 s'(t)=鑲屽摋鍐犵嫏鏀夌即鍦枩姘﹂搯(t^3)'=3t^2 鎵浠ワ紝t=2s鏃剁殑鐬椂閫熷害涓 s'(2)=3脳2^2=12(m/s)
绛旓細v(t)=6t + 2 v(0)=2;v(4)=24+2=26 骞冲潎閫熷害v=锛2+26锛/2=14
绛旓細v(t)=6t + 2 v(0)=2;鐬椂閫熷害v(4)=24+2=26 骞冲潎閫熷害v=锛2+26锛/2=14 鍚屽浣犲ソ锛屽鏋滈棶棰樺凡瑙e喅锛岃寰楀彸涓婅閲囩撼鍝~~鎮ㄧ殑閲囩撼鏄瀵规垜鐨勮偗瀹殈璋㈣阿鍝