Question

A runner completes five rounds of a circular track of radius 200 m. Find the distance covered by the runner in five rounds. Find his displacement after he completes 4.5 rounds.​

Answer 1

$\huge\tt\fcolorbox{cyan}{Lavender}{ ANSWER♡࿐}$

• Distance and displacement are two terms that appear to be identical but have quite different meanings and definitions. The term “distance” relates to how much ground an object has covered during its motion, whereas “displacement” refers to how far out of place is an object.

$\sf\red{Given\:Parameters}$

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.

Displacement = ??

Speed = Distance/Time

${\huge{\underline{\small{\mathbb{\pink{Tatal \ time \ athlete \ movie \ -2 min \ 20 seconds}}}}}}$

2 min 20 sec $\frac{2}{×60} + 20$

$\frac{2 min}{20} =140$

Find the distance covered in one round

Distance covered in one round = Circumference of a circle.

Distance covered in one round = πR

Distance covered in one round = 2 × 100 × π

Distance covered in one round = 200π

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

Number of rounds completed in 140s = 140/40

Number of rounds completed in 140s = 3.5

Distance covered = 3.5 × circumference

Distance covered = 3.5 × 2πr

Distance covered = 3.5 × 2 × 3.14 × 100

Distance covered = 2198 ≈ 2200 m

Displacement in 2 mins that is 120 s will be zero because the athlete will complete 3 rounds and at that time initial position and final position will be the same

But, later the next 20 s the displacement will be equal to the diameter of the circular track which is 200 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.

$\huge\star\red{200_m}$

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$\sf\red{Thank\:you!}$