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STD 11 - 2. motion in straight line — JEE STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceJEESTD 11 - 2. motion in straight line4 Marks
Question
Between the two stations a train accelerates uniformly at first, then moves with constant velocity and finally retards uniformly. If the ratio of the time taken be $1 : 8 : 1$ and the maximum speed attained be $60\,km/h,$ then what is the average speed over the whole journey.......$km/h$
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Answer

c
$A$ ve. speed $=\begin{array}{ll}{\text { total distance }} & {\text { area under } v-\text { t graph }} \\ {\text { total time }} & {\text { totaltime }}\end{array}$

$=\frac{\frac{1}{2}(8 t+10 t) \times 60}{10 t}=54 k m / h r$

average speed for $A$ to $B=\frac{0+60}{2}=30 \mathrm{km} / \mathrm{hr}$

average speed for $C$ to $D=\frac{60+0}{2}=30 \mathrm{km} / \mathrm{hr}$

average speed for $A$ to $D$

$v_{\operatorname{arc}}=\frac{30 \times t+60 \times 8 t+30 \times t}{t+8 t+t}$

$=\frac{30+480+30}{10}=\frac{540}{10}=54 \mathrm{km} / \mathrm{hr}$

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