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题目一只老鼠从洞口爬出后沿一直线运动,其速度大小与其离开洞口的距离成反比,当其到达距洞口为d1的点A时,速度为v1.若点B离洞口的距离为d2(d2>d1),求老鼠由点A运动到点B所需时间.解析:如右图中的图线与横轴所围面积的数值正是老鼠经过一定位移所需的时间.如右图,取一窄条,其宽度Δx很小,此段位移所需时间Δt也很小,可以认为在此短时间内,老鼠的速度改变Δv很小,此图中窄条的面积为S,这正是老鼠经过一段位移所需时间.故图中图
Problem A mouse moves in a straight line after it crawls out of the hole and its velocity is inversely proportional to its distance from the hole. When it reaches point A at hole d1, the velocity is v1. If point B is a distance d2 from the hole (d2> d1) and find the time it takes for the mouse to move from point A to point B. Analysis: As shown in the figure on the right and the axis of the area enclosed by the value of the rat is a certain displacement of the time required. , Take a narrow strip, the width Δx is very small, the time required for this segment Δt is also very small, can be considered in this short period of time, the mouse speed change Δv is small, the narrow area in this diagram S, which It is the mouse after a period of time required for displacement