Solved: PHYSICS Question for NEET

NEET PHYSICSEasy

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

\frac{3v}{4}

\frac{v}{3}

\frac{2v}{3}

\frac{4v}{3}

Define Average Speed: Average speed is defined as the ratio of the total distance traveled to the total time taken . $v_{avg} = \frac{\text{Total Distance}}{\text{Total Time}}$
Set Up Variables: Let the total distance be $2d$ . The vehicle travels the first half distance ( $d$ ) with speed $v_1 = v$ and the second half distance ( $d$ ) with speed $v_2 = 2v$ .
Calculate Time Intervals: Time for the first half ( $t_1$ ) = $\frac{\text{distance}}{\text{speed}} = \frac{d}{v}$ Time for the second half ( $t_2$ ) = $\frac{d}{2v}$
Calculate Total Time: $T = t_1 + t_2 = \frac{d}{v} + \frac{d}{2v} = \frac{2d + d}{2v} = \frac{3d}{2v}$
Calculate Average Speed: $v_{avg} = \frac{2d}{\frac{3d}{2v}} = \frac{2d \times 2v}{3d} = \frac{4v}{3}$ Alternative Formula: For equal distances covered at speeds $v_1$ and $v_2$ , the average speed is the harmonic mean: $v_{avg} = \frac{2v_1v_2}{v_1 + v_2} = \frac{2(v)(2v)}{v + 2v} = \frac{4v^2}{3v} = \frac{4v}{3}$ .

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