Motion In One Dimension Question 10

Question 10 - 01 February - Shift 1

An object moves with speed $v_1, v_2$, and $v_3$ along a line segment $AB, BC$ and $CD$ respectively as shown in figure. Where $A B=B C$ and $A D=3 A B$, then average speed of the object will be :

(1) $\frac{(v_1+v_2+v_3)}{3}$

(2) $\frac{v_1 v_2 v_3}{3(v_1 v_2+v_2 v_3+v_3 v_1)}$

(3) $\frac{3 v_1 v_2 v_3}{v_1 v_2+v_2 v_3+v_3 v_1}$

(4) $\frac{(v_1+v_2+v_3)}{3 v_1 v_2 v_3}$

Show Answer

Answer: (3)

Solution:

Formula: Average velocity if n velocities are given

$AB=x$

$BC=x$

$2 x+CD=3 x$

$CD=x$

$ =\frac{3 x}{\frac{x}{v_1}+\frac{x}{v_2}+\frac{x}{v_3}}=\frac{3 v_1 v_2 v_3}{v_2 v_3+v_1 v_3+v_1 v_2} $