A car covers A B distance with first one-third at velocity v 1 m s - 1 , second one-third at v 2 m s - 1 and last one-third at v 3 m s - 1 . If v 3 = 3 v 1 , v 2 = 2 v 1 and v 1 = 11 m s - 1 , then the average velocity of the car is _____ m s - 1 .

Step-by-step solution

Let the total distance be d . Time taken to cover 1 3 rd of total distance is t 1 = d 3 v 1 . Time taken to cover 1 3 rd of total distance is t 2 = d 3 v 2 . Time taken to cover 1 3 rd of total distance is t 3 = d 3 v 3 . Average speed = Total   distance Total   time v a v g = d d 3 v 1 + d 3 v 2 + d 3 v 3 ⇒ v a v g = 3 v 1 v 2 v 3 v 1 v 2 + v 2 v 3 + v 3 v 1 Here, v 1 = 11   m   s - 1 , then, v 3 = 33   m   s - 1 ,   v 2 = 22     m   s - 1 V avg   = 3 &#