Question

If a particle travels a linear distance at speed $v_{1}$ and comes back along the same track at speed $v_{2}$
(1) Its average speed is arithmetic mean $\left(v_{1}+v_{2}\right) / 2$
(2) Its average speed is harmonic mean $2 v_{1} v_{2} /\left(v_{1}+v_{2}\right)$
(3) Its average speed is geometric mean $\sqrt{v_{1} v_{2}}$
(4) Its velocity is zero

• A. 1, 2 and 3 are correct
• B. 1 and 2 are correct
• C. 2 and 4 are correct
• D. 1 and 3 are correct

Answer 1

Answer: (C)

If a particle moves a distance $l$ at speed $v_{1}$ and comes back with speed $v_{2}$, then its average speed
$v_{ av } =\frac{\Delta s}{\Delta t}=\frac{l+l}{\frac{l}{v_{1}}+\frac{l}{v_{2}}}=\frac{2 v_{1} v_{2}}{v_{1}+v_{2}} $
$=$ harmonic mean
Further $\vec{ v } _{av }=\frac{\Delta \vec{ r }}{\Delta t}=\frac{\vec{1}-\vec{1}}{\frac{l}{v_{1}}+\frac{l}{v_{2}}}=0$