A horse rider covers half distance with 5,m / s speed. remaining part of distance was travelled with

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2.Motion in Straight Line

hard

A horse rider covers half the distance with $5\,m / s$ speed. The remaining part of the distance was travelled with speed $10\,m / s$ for half the time and with speed $15 m / s$ for other half of the time. The mean speed of the rider averaged over the whole time of motion is $\frac{x}{7}\,m / s$. The value of $x$ is

A$25$

B$20$

C$26$

D$50$

(JEE MAIN-2023)

Solution

$t _{ AB }=\frac{ x }{5 m / s }$
In motion $BC$
$x = d _1+ d _2$
where $d _1 , d _2$ we the distance travelled with $10\,m / s$ and $15\,m / s$ respectively in equal time intervals
$\frac{' t^{\prime}}{2} \text { each }$
$d_1=\frac{10 t}{2}, d_2=\frac{15 t }{2}$
$d_1+d_2=x=\frac{t}{2}(10+15)=\frac{25 t }{2}$
$< v >=\frac{2 x }{\frac{ x }{5}+\frac{2 x }{25}}=\frac{2 \times 25}{5+2}=\frac{50}{7} m / s$
Ans. : $50$

Standard 11

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Solution

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