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(D) Let the total distance be $S$.The vehicle travels the first half distance $(S/2)$ with speed $v_1 = v$.The time taken for the first half is $t_1 =

Vedclass · Accepted Answer

$\frac{4v}{3}$

Vedclass · Answer

(D) Let the total distance be $S$.The vehicle travels the first half distance $(S/2)$ with speed $v_1 = v$.The time taken for the first half is $t_1 = \frac{S/2}{v} = \frac{S}{2v}$.The vehicle travels the remaining half distance $(S/2)$ with speed $v_2 = 2v$.The time taken for the second half is $t_2 = \frac{S/2}{2v} = \frac{S}{4v}$.The average speed is defined as the total distance divided by the total time:$V_{avg} = \frac{	ext{Total Distance}}{	ext{Total Time}} = \frac{S}{t_1 + t_2}$$V_{avg} = \frac{S}{\frac{S}{2v} + \frac{S}{4v}} = \frac{S}{\frac{2S + S}{4v}} = \frac{S}{\frac{3S}{4v}}$$V_{avg} = \frac{4v}{3}$

$A$ vehicle travels half the distance with speed $v$ and the remaining distance with speed $2v$. Its average speed is:

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