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 $2v_1{v}_2/\left(v_1+v_2\right)$
(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
$v_{av}=\frac{\Delta s}{\Delta t}=\frac{l+l}{\frac{l}{v_1}+\frac{l}{v_2}}=\frac{2v_1{v}_2}{v_1+v_2}$
$=$ harmonic mean
Further ${\vec{v}}_{av}=\frac{\Delta \vec{r}}{\Delta t}=\frac{\vec{1}-\vec{1}}{\frac{l}{v_1}+\frac{l}{v_2}}=0$