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
$AB=x$
$BC=x$
$2 x+CD=3 x$
$CD=x$
$ v=\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} $
