Verified Solution • 2025–26 Session moderate

QJEEM23Ph4923: JEE Main 2023 Physics - Class 11 JEEM23Ph4923 Solution: A horse rider covers half the distance with speed. The…

A horse rider covers half the distance with 5 m/s5 \mathrm{~m} / \mathrm{s} speed. The remaining part of the distance was travelled with speed 10 m/s10 \mathrm{~m} / \mathrm{s} for half the time and with speed 15 m/s15 \mathrm{~m} / \mathrm{s} for other half of the time. The mean speed of the rider averaged over the whole time of motion is x7 m/s\frac{x}{7} \mathrm{~m} / \mathrm{s} . The value of xx is ___________.

Step-by-Step Verified Solution

⇒t1=S25\Rightarrow {t_1} = {{{S \over 2}} \over 5} ........ (1)

Also, S2=10t22+15t22{S \over 2} = {{10{t_2}} \over 2} + {{15{t_2}} \over 2}

⇒t2=S25\Rightarrow {t_2} = {S \over {25}} ....... (2)

⇒\Rightarrow Mean speed =St1+t2= {S \over {{t_1} + {t_2}}}

=SS10+S25=25035= {S \over {{S \over {10}} + {S \over {25}}}} = {{250} \over {35}} m/s =507= {{50} \over 7} m/s

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