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