Question

An insect moves along the sides of a wall of dimension $12m\times 5m$, starting from one corner and reaches the diagonally opposite corner. If the insect takes $2s$ for its motion, then find the ratio of average speed to average velocity of insect.

• A. $17:13$
• B. $12:5$
• C. $13:5$
• D. $17:12$

Answer 1

Answer: (A)

Given: The dimension of the wall is $12m\times 5m$
Total time taken $=2s$
Total distance $=AB+BC=12m+5m=17m$

Total displacement $=AC=\sqrt{A{B}^2+B{C}^2}$ (By Pythagoras theorem)
or, $AC=\sqrt{5^2+{12}^2}$=$\sqrt{169}=13m$

$\text{Average speed}=\frac{\text{Total distance}}{\text{Total time}}$
$\text{Average speed}=\frac{17}{2}m/s$

$\text{Average velocity}=\frac{\text{Total displacement}}{\text{Total time}}$
$\text{Average velocity}=\frac{13}{2}m/s$

$\therefore \frac{\text{Average speed}}{\text{Average velocity}}=\frac{17}{13}$