An Athelete completes one round of a circular track of radius 'R' in 40 seconds. What will be his displacement at the end of 2 minutes 20 seconds ?
one revolution completed in = 40 sec(s)
no. of revolutions in 2 min(s)20sec(s)= 140/40 = 3.5
i.e. three and a half revolutions.
then displacement is equal to diameter
Time taken to complete 1 revolution=40s
total time given=2min20s=(2*60)+20s=140s (1 minute=60s)
no. of revolutions=140/40=3.5
in 3 full rounds, displacement==0
but for the remaining .5 path left, the athlete can travel along the diameter of the circle as displacement is the2R shortest path taken
thus displacement=diameter of circle=
Since,rotation in 40 s=1
Therefore, rotation in 1s=140
∴ rotation in 140s=140×140=3.5
Therefore, in 3.5 rotations athlete will be just at the opposite side of the circular track, i.e. at a distance equal to the diameter of the circular track which is equal to 200 m.
Distance covered in 2 m 20 s = 2198 m
And, displacement after 2 m 20 s = 200m