Question

An insect moves along a circular path of radius $10\text{cm}$ with a constant speed. If it takes $1\text{minute}$ to move from a point on the path to the diametrically opposite point, then what is the distance it travels and the average velocity of the insect respectively?

• A. $3.14\text{cm},0.2\text{cm/sec}$
• B. $31.4\text{cm},0.33\text{cm/sec}$
• C. $0.314\text{cm},0.5\text{cm/sec}$
• D. $314\text{cm},0.1\text{cm/sec}$

Answer 1

The correct option is B $31.4\text{cm},0.33\text{cm/sec}$

The distance travel by the insect is equal to half the circumference of the circular path as the final position is diametrically opposite. Therefore distance travelled by the insect is
distance $=\frac{2\times \pi \times 10}{2}=31.4\text{cm}$
Now the average velocity is defined as
$v=\frac{\text{displacement}}{\text{total time taken}}$
The displacement of the insect is the distance is the shortest distance between its initial and final positions. This is equal to the diameter of the circular path, therefore
$v=\frac{20}{1}\text{cm/min}=\frac{20}{60}\text{cm/s}=0.33\text{cm/s}$
Therefore, option B is correct