Question

An athlete completes one round of a circular track of diameter200 m in 40 s. What will be the distance covered and the displacement at the end of 2 minutes 20 s?​

Answer 1

$\large{ \sf\underline{Solution- }}$

Here it is given that,

• Diameter of circular track = 200 m
• So, radius = 100 m
• Time taken by Athlete to complete one round = 40 sec

➢ We have to find the distance covered and displacement at the end of 2 min 20 sec.

Now,

Total time athlete moves = 2 min 20 seconds

⟹ 2 × 60 seconds + 20 seconds

⟹ 120 seconds + 20 seconds

⟹ 140 seconds

Now,

As in 40 seconds the athlete completes one round.

So, in 140 seconds the athlete will completes :

$\rm \implies \: \dfrac{140}{40} = 3.5 \: rounds$

Now,

⟹ Distance covered in 140 seconds = 2πr × 3.5

$\rm \implies \: 2 \times \dfrac{22}{7} \times 100 \times 3.5$

$\rm \implies \: \dfrac{2 \times 22 \times 100 \times 35}{7 \times 10}$

$\rm \implies \: 2 \times 22 \times 10 \times 5$

$\bf \implies \: 2200 \: m$

At the end of the athlete's motion, the athlete will be diametrically opposite position.

⟹ Displacement = diameter = 200 m

Answer 2

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

Total time athlete moves – 2 min 20 seconds

2 min 20 seconds = 2 × 60 + 20

2 min 20 seconds = 140 seconds

Find the distance covered in one round

Distance covered in one round = Circumference of a circle.

Distance covered in one round = 2πr

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.

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.