Question

An ant moves along the square loop of side $a\text{m}$. If it moves along path $ABC$, starting from $A$ to reach at the point $C$ in $2\text{s}$.

The average velocity of ant will be

• A. Avergae velocity of ant is $a\text{m/s}$ along $ABC$
• B. Avergae velocity of ant is $\frac{a}{\sqrt{2}}\text{m/s}$ along $AC$
• C. Avergae velocity of ant is $\frac{3a}{\sqrt{2}}\text{m/s}$ along $BC$
• D. Average velocity of ant is zero.

Answer 1

The correct option is B Avergae velocity of ant is $\frac{a}{\sqrt{2}}\text{m/s}$ along $AC$

The displacement of ant will be the length of diagonal $AC$.
$\Delta S=AC=\sqrt{2}a\text{m}$
$\Delta t=2\text{s}$
${\text{velocity}}_{\text{avg}}=\frac{\Delta S}{\Delta t}$
$\therefore {\text{velocity}}_{\text{avg}}=\frac{\sqrt{2}a\text{m}}{2\text{s}}=\frac{a}{\sqrt{2}}\text{m/s}$
This is the required magnitude of average velocity. However, the direction of average velocity will be along the direction of displacement$(A\to C)$.
$\Rightarrow$ Avergae velocity of ant is $\frac{a}{\sqrt{2}}\text{m/s}$ along $AC$