Diameter of circular track $( D )=200\, m$

Radius of circular track $(r)=200 / 2=100 \,m$

Time taken by the athlete for one round $(t)=40\,s$

Distance covered by athlete in one round $(s)=2 \pi r$

$=2 \times(22 / 7) \times 100$

Speed of the athlete $(v)=$ Distance $/$ Time

$=(2 \times 2200) /(7 \times 40)$

$=4400 / 7 \times 40$

Therefore, Distance covered in $140 \,s =$ Speed $( s ) \times$ Time $(t)$

$=4400 /(7 \times 40) \times(2 \times 60+20)$

$=4400 /(7 \times 40) \times 140$

$=4400 \times 140 / 7 \times 40$

$=2200 \,m$

Number of round in $40 \,s =1$ round

Number of round in $140 \,s =140 / 40 =3^{1 / 2}$

After taking start from position $X$,the athlete will be at postion $Y$ after $3^{1 / 2}$ rounds as shown in figure.

Hence, Displacement of the athlete with respect to initial position at $X= XY$

$=$ Diameter of circular track

$= 200\, m$