Question

An athlete completes one round of a circular track of diameter $200 \;m$ in $40 \;s$. What will be the distance covered and the displacement at the end of $2$ minutes $20$ $s$?

Answer 1

Diameter of circular track (D) = $200$ $m$
Radius of circular track (r) = $\frac{200 }{ 2}$ = $100$ $m$
Time taken by the athlete for one round (t) = $40$ $s$
Distance covered by athlete in one round (s) = $2\pi r$
= $2 \times \bigg( \frac{22}{ 7} \bigg) \times 100$
Speed of the athlete (v) = $\frac{Distance }{ Time}$

= $\frac{(2 \times 2200) }{ (7 \times 40)}$

= $\frac{4400 }{ 7} \times 40$
Therefore, Distance covered in $140$ $s$ = Speed (s) × Time(t)
= $\frac{4400 }{ (7 \times 40) }\times (2 \times 60 + 20)$

= $\frac{4400 }{ ( 7 \times 40)} \times 140$

= $4400 \times \frac{140 }{7} \times 40$
= $2200$ $m$
Number of round in $40$ $s$ = $1$ round
Number of round in $140$ $s$ =$\frac{140}{40}$
=$3 \frac{1 }{2}$

Hence, Displacement of the athlete with respect to initial position at x= xy
= Diameter of circular track
= $200$ m