A car covers AB distance with first one-third at velocity v1 ms - 1, second one-third at v2 ms - 1 and last one-third at v3 ms - 1. If v3 = 3v1, v2 = 2v1 and v1 = 11 ms - 1 then the average velocity of the car is \underline\hspace2cm ms - 1.

Motion in A Straight Line PYQ — JEE Main 2022 · 28 Jun · Shift 2 · Q77 with Solution

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Correct answer: 18

Let the total distance be $D$ .
The car covers the distance in three equal parts, so each part is: $\frac{D}{3}$
Given: $v_1 = 11\ \text{m s}^{-1}$ $v_2 = 2v_1 = 22\ \text{m s}^{-1}$ $v_3 = 3v_1 = 33\ \text{m s}^{-1}$
Time taken in each one-third part: $t_1 = \frac{D/3}{v_1} = \frac{D}{33}$ $t_2 = \frac{D/3}{v_2} = \frac{D}{66}$ $t_3 = \frac{D/3}{v_3} = \frac{D}{99}$
Total time: $T = t_1+t_2+t_3 = \frac{D}{33}+\frac{D}{66}+\frac{D}{99}$ Taking LCM $=198$ , $T = \frac{6D+3D+2D}{198} = \frac{11D}{198} = \frac{D}{18}$
Average velocity is: $v_{\text{avg}} = \frac{\text{total distance}}{\text{total time}} = \frac{D}{D/18} = 18\ \text{m s}^{-1}$
Therefore, the required integer answer is: $\boxed{18}$