A point object traverses half the distance with velocity v0. The remaining part of the distance is covered with velocity v1 for the half time and with velocity v2 for the rest half. The average velocity of the object for the whole journey is

Question

A point object traverses half the distance with velocity v0. The remaining part of the distance is covered with velocity v1 for the half time and with velocity v2 for the rest half. The average velocity of the object for the whole journey is (A) 2 v1(v0+v2) /(v0+2 v1+2 v2) (B) 2 v(v0+v1) /(v0+v1+v2) (C) 2 v0(v1+v2) /(v1+v2+2 v0) (D) 2 v2(v0+v1) /(v1+2 v2+v0)

Tardigrade Admin · Accepted Answer

<img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/physics/43fb4b70fd26bc38ece4bac3828025e3-.png" /> v avg for second half =( v 1+ v 2/2) vavg for total =(2(v0)((v1+v2/2))/v0+(v1+v2)2) v text avg =(2 v0(v1+v2)/2 v0+v1+v2)

Q. A point object traverses half the distance with velocity $v_{0}$ . The remaining part of the distance is covered with velocity $v_{1}$ for the half time and with velocity $v_{2}$ for the rest half. The average velocity of the object for the whole journey is

$2 v_{1} (v_{0} + v_{2}) / (v_{0} + 2 v_{1} + 2 v_{2})$

$2 v (v_{0} + v_{1}) / (v_{0} + v_{1} + v_{2})$

$2 v_{0} (v_{1} + v_{2}) / (v_{1} + v_{2} + 2 v_{0})$

$2 v_{2} (v_{0} + v_{1}) / (v_{1} + 2 v_{2} + v_{0})$

$v_{a vg}$ for second half $= \frac{v _{1} + v _{2}}{2}$
$v_{a vg}$ for total $= \frac{2 ( v _{0} ) ( \frac{v _{1} + v _{2}}{2} )}{v _{0} + \frac{v _{1} + v _{2}}{2}}$
$v_{avg} = \frac{2 v _{0} ( v _{1} + v _{2} )}{2 v _{0} + v _{1} + v _{2}}$

Q. A point object traverses half the distance with velocity v0​. The remaining part of the distance is covered with velocity v1​ for the half time and with velocity v2​ for the rest half. The average velocity of the object for the whole journey is

2v1​(v0​+v2​)/(v0​+2v1​+2v2​)

2v(v0​+v1​)/(v0​+v1​+v2​)

2v0​(v1​+v2​)/(v1​+v2​+2v0​)

2v2​(v0​+v1​)/(v1​+2v2​+v0​)