题目
The diagram shows the velocity-time graph for the motion of an athlete. The athlete runs in a straight line from point to point , runs back to point and finishes at point . The graph consists of four straight line segments.
(a) Find the deceleration of the athlete seconds after leaving .
(b) Find the total distance travelled by the athlete.
题目中文翻译
图中显示一名运动员运动的速度—时间图像。运动员从点 沿直线跑到点 ,再跑回点 ,最后在点 结束。图像由四条直线段组成。
(a) 求运动员离开 后 秒时的减速度。
(b) 求运动员运动的总路程。
原卷通用作答要求
Answer all questions. You should use a calculator where appropriate.
You must show all necessary working clearly; no marks will be given for unsupported answers from a calculator.
Give non-exact numerical answers correct to 3 significant figures, or 1 decimal place for angles in degrees, unless a different level of accuracy is specified in the question.
请回答所有题目。适当时应使用计算器。必须清楚展示所有必要的计算过程;仅给出计算器答案而没有过程,不予评分。除非题目另有精度要求,非精确数值答案保留 3 位有效数字,以度为单位的角度保留 1 位小数。
Where a numerical value for the acceleration due to gravity () is needed, use .
需要使用重力加速度 的数值时,取 。
解答
(a)
解法一
思路
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7秒位于5至15秒的下降直线段,斜率是加速度,减速度取大小。
答题过程
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At , the acceleration is the gradient of the segment from to :
Thus the deceleration is .
(b)
解法一
思路
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每段往返的路程是对应三角形面积大小,负速度面积也按正值相加。
答题过程
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The graph forms three triangles, each with base 10 seconds and height in magnitude. The total distance is