Question

A)Particle cover half the distance with velocity 60km/hr.Remaining part of distance was covered with velocity 15km/hr, for half of the time and with velocity 45km/hr,for other half of time . Find the average speed ? A) 25km/hr B) 40km/hr C) 30km/hr D) 20km/hr​

Answer 1

$\sf{\bold{\blue{\underline{\underline{Given}}}}}$

Particle cover half the distance with velocity 60km/hr.

Remaining part of distance was covered with velocity 15km/hr, for half of the time

and with velocity 45km/hr,for other half of time .⠀⠀⠀⠀

$\sf{\bold{\red{\underline{\underline{To\:Find}}}}}$

Find the average speed????⠀⠀⠀⠀

$\sf{\bold{\purple{\underline{\underline{Solution}}}}}$

1st half velocity=$V_0=60$km/hr.

remaining,

 $V_1=15$ km/hr.

$V_2=45$km/hr.

Let total distance travelled =s

so..,

travelled half time taken=$t_1$

second half=$t_2$

Distance travelled in 1st half $\rightsquigarrow$$\tt{\frac{S}{2}}$

$\rightsquigarrow$ $\tt{t_1=\frac{\frac{S}{2}}{V_0}=\frac{s}{2V_0}}$

Time taken to cover second half =$\tt{t_2}$

$\therefore$$\huge\tt{\frac{s}{2}=\frac{t_2 v_1}{2} + \frac{t_2 V_2}{2}}$

$\rightsquigarrow$ $\tt{s=t_2(V_1+V_2) }$

$\rightsquigarrow$ $\tt{t_2=( \frac{s}{V_1+V_2} )}$

Total time taken, $t_1+t_2$

$\rightsquigarrow$ $\tt{\frac{s}{2V_0}+\frac{s}{(V_1+V_2)}}$

$\boxed{\underline{\underline{\mathcal\color{gold}{Avarage ~speed=\frac{Total ~distance}{Total ~time}}}}}$

$\rightsquigarrow$ $\huge\tt{\frac{S}{\frac{s}{2V_0}+\frac{s}{(V_1+V_2)}}}$

Average speed

$\rightsquigarrow$$\huge\tt{\frac{2V_0(V_1+V_2)}{2V_0+V_1+V_2}}$

so..

putting the value..

we get,

$\rightsquigarrow$ $\tt{\frac{2×60(15+45)}{2×60+15+45}}$

$\rightsquigarrow$ $\tt{\frac{120×60}{120+60}}$

$\rightsquigarrow$ $\tt{\frac{720}{180}}$

$\rightsquigarrow$ $\rightsquigarrow{40}$

$\sf{\bold{\green{\underline{\underline{Answer}}}}}$

⠀⠀⠀⠀

Avarage speed.. $\rightsquigarrow{\pink{40km/hr.}}$

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