question_answer

There is a square field of side a units. A tortoise starts from one corner and reaches the diagonally opposite corner of the field in a time interval of t. Find the magnitude of the average velocity of the tortoise.

Answer:

Let ABCD be the square field, each side measuring a units. Let the tortoise start from B and reach, the diagonally opposite corner in a time interval of t. \[Average\,\,velocity=\frac{Total\,\,displacement}{Total\,time}\] From the figure, DB is the displacement of the tortoise, \[DB=\sqrt{{{a}^{2}}+{{a}^{2}}}=\sqrt{2{{a}^{2}}}=\sqrt{2}a\] Average velocity of the tortoise \[=\frac{\sqrt{2}a}{t}\]