Question

a body complete one round of a cricle of radius 'r' in 20sec. the displacement of the body after 45 seconds

Answer 1

In 20 sec displacement will be zero as the particle is back to its same place, again afer20 sec it will come back to its place,so after 40 sec displacement will be zero. In 10 sec it will complete semicircle that means in 5 sec it will complete quarter circle,so after 45 sec particle will be at quarter position of circle. Hence displacement is shortest distance between final and initial position I.e. drawing a line will be a hypotenuse for a right angle triangle with other two sides as radius. Hence answer will be √2R.
If it completed 11 round in 2020 seconds, it completes 2.252.25 rounds in 4545 seconds. Therefore, displacement is the hypotenuse of the isosceles right angled triangle formed by the radii and the line joining the initial and the final position points. Using Pythagoreas theorem, where ss is the displacement,

s=R2+R2−−−−−−−√=2R2−−−√=2–√Rs=R2+R2=2R2=2R.