A horse rider covers half the distance with $5 \mathrm{~m} / \mathrm{s}$ speed. The remaining part of the distance was travelled with speed $10 \mathrm{~m} / \mathrm{s}$ for half the time and with speed $15 \mathrm{~m} / \mathrm{s}$ for other half of the time. The mean speed of the rider averaged over the whole time of motion is $\frac{x}{7} \mathrm{~m} / \mathrm{s}$. The value of $x$ is ___________.
Answer (integer)
50
Solution
<p>$\Rightarrow {t_1} = {{{S \over 2}} \over 5}$ ........ (1)</p>
<p>Also, ${S \over 2} = {{10{t_2}} \over 2} + {{15{t_2}} \over 2}$</p>
<p>$\Rightarrow {t_2} = {S \over {25}}$ ....... (2)</p>
<p>$\Rightarrow$ Mean speed $= {S \over {{t_1} + {t_2}}}$</p>
<p>$= {S \over {{S \over {10}} + {S \over {25}}}} = {{250} \over {35}}$ m/s $= {{50} \over 7}$ m/s</p>
About this question
Subject: Physics · Chapter: Kinematics · Topic: Motion in a Straight Line
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