Question

An athlete complete one round of a circular track of diameter 200m in 40sec. What will be the distance covered and displacement​

Answer 1

$\underline{\underline{\maltese\: \: \textbf{\textsf{ Complete Question:-}}}}$

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

$\underline{\underline{\maltese\: \: \textbf{\textsf{ Answer:-}}}}$

$\sf\small{ \underline{\underline\red{ \pmb{Given:-}}}}$

• The diameter of the circular track = 200 m
• Radius (r) = 200/2
• r = 100 m

Time is taken by an athlete to complete one round = 40 seconds.

$\sf\small{ \underline{\underline\red{ \pmb{To \: find:-}}}}$

Displacement = ??

$\sf\small{ \underline{\underline\red{ \pmb{Formula \: that \: we \: used:-}}}}$

$\begin{gathered} \large{\leadsto} \underline{ \boxed{ \sf \pink{ Speed = \frac{Distance}{Time}}}}\\ \end{gathered}$

Total time athlete moves – 2 min 20 seconds

2 min 20 seconds = 2 × 60 + 20 = 140 seconds

Need to find the distance covered in one round

Distance covered in one round = Circumference of circle

$\sf \: Distance \: covered \: in \: one \: round \\\\ \sf= 2πr\\ \\ \sf \: = 2$

$\sf \: Distance \: covered \: in \: one \: round \\\\ \sf = 2 × 100π \\\\ \sf \: =200π$

• Time is taken by an athlete to complete one round = 40 seconds.

$\sf \: Number \: of \: rounds \: completed \: in \: 140s \\\\ = \sf \: \cancel\frac{140}{40} \\\\ \sf = 35$

$\sf \: Distance \: covered = 3.5 × circumference \\\\ \sf = 3.5 × 2πr \\\\\sf= 3.5 × 2 × 3.14 × 100 \\\\ = \underline{\boxed{ \red{\sf 2200 m}}}$

Hence, the distance covered at the end of 2 min 20 seconds is 2200 m or 22 km and displacement is 200 m as it returns to the initial position.