An object moves with speed v1, v2 and v3 along a line segment AB , BC and C D respectively as shown in figure. Where AB = BC and AD =3 AB, then average speed of the object will be:

Question

An object moves with speed v1, v2 and v3 along a line segment AB , BC and C D respectively as shown in figure. Where AB = BC and AD =3 AB, then average speed of the object will be: (A) ((v1+v2+v3)/3) (B) (3 v1 v2 v3/(v1 v2+v2 v3+v3 v1)) (C) ((v1+v2+v3)/3 v1 v2 v3) (D) (v1 v2 v3/3(v1 v2+v2 v3+v3 v1))

Tardigrade Admin · Accepted Answer

AB =x BC =x 2 x+ CD =3 x CD = x langle v rangle=(3 x/(x)v1+(x)v2+(x/v3)=(3 v1 v2 v3/v2 v3+v1 v3+v1 v2)

Q. An object moves with speed $v_{1}, v_{2}$ and $v_{3}$ along a line segment $A B, BC$ and $C D$ respectively as shown in figure. Where $A B = BC$ and $A D = 3 A B$ , then average speed of the object will be:

$\frac{( v _{1} + v _{2} + v _{3} )}{3}$

$\frac{3 v _{1} v _{2} v _{3}}{( v _{1} v _{2} + v _{2} v _{3} + v _{3} v _{1} )}$

$\frac{( v _{1} + v _{2} + v _{3} )}{3 v _{1} v _{2} v _{3}}$

$\frac{v _{1} v _{2} v _{3}}{3 ( v _{1} v _{2} + v _{2} v _{3} + v _{3} v _{1} )}$

$A B = x$
$BC = x$
$2 x + C D = 3 x$
$C D = x$
$⟨ v ⟩ = \frac{3 x}{\frac{x}{v _{1}} + \frac{x}{v _{2}} + \frac{x}{v _{3}}} = \frac{3 v _{1} v _{2} v _{3}}{v _{2} v _{3} + v _{1} v _{3} + v _{1} v _{2}}$

Q. An object moves with speed v1​,v2​ and v3​ along a line segment AB,BC and CD respectively as shown in figure. Where AB=BC and AD=3AB, then average speed of the object will be:

3(v1​+v2​+v3​)​

(v1​v2​+v2​v3​+v3​v1​)3v1​v2​v3​​

3v1​v2​v3​(v1​+v2​+v3​)​

3(v1​v2​+v2​v3​+v3​v1​)v1​v2​v3​​