Question

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

• A. $2 v_{1}\left(v_{0}+v_{2}\right) /\left(v_{0}+2 v_{1}+2 v_{2}\right)$
• B. $2 v\left(v_{0}+v_{1}\right) /\left(v_{0}+v_{1}+v_{2}\right)$
• C. $2 v_{0}\left(v_{1}+v_{2}\right) /\left(v_{1}+v_{2}+2 v_{0}\right)$
• D. $2 v_{2}\left(v_{0}+v_{1}\right) /\left(v_{1}+2 v_{2}+v_{0}\right)$

Answer 1

Answer: (C)

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