Question

An athlete completes one round of circular track of diameter 200m in 4 sec. what will be the distance covered and the displacement at the end of 2 minutes 20 seconds?​

Answer 1

$\huge{\underline{\tt{\red{Answer-}}}}$200 m

$\small{\underline{\tt{\blue{Given-}}}}$Diameter of circular track = 200 m

Radius, r = 200/2 = 100 m

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

$\huge{\underline{\tt{\blue{Solution-}}}}$

Formula to be used :-

$\boxed{speed = \frac{distance}{time} }$

Circumference of circle = $\boxed{2 \pi r} }$

2 min 20 seconds = 140 seconds

Number of rounds = 140/4 = 35

⇒ Distance covered = 35 × circumference

⇒ Distance covered = 35 × 2 × 22/7 × 100

⇒ Distance covered = 5 × 2 × 22 × 100

⇒ Distance covered = 22000 m

Hence,

the distance covered at the end of 2 min 20 seconds is 22000 m or 22 km.

And displacement is 200 m as it return to initial position again.

Answer 2

✬ Distance = 2200 m ✬

✬ Displacement = 200 m ✬

Explanation:

Given:

• Diameter of circular track is 200 m.
• Time take by athlete to cover 200 m is 4 seconds.

To Find:

• Distance covered and displacement at the end of 2 minutes 20 seconds.

Solution: Diameter of track is 200 m therefore,

➟ Radius of track = d/2 = 200/2 = 100 m

➟ Time taken to cover 1 round = 40 seconds and Total time taken 2 minutes 20 seconds.

• 1 min = 60 seconds

∴ 2 min 20 sec = 2(60) + 20

=> 140 seconds.

Distance covered by athelete in one round will be equal to the circumference of circle.

★ Circumference of circle = 2πr ★

$\implies{\rm }$ Distance covered = 2π(100)

$\implies{\rm }$ Distance covered = 200π

Thus,

• Distance covered in 40 sec = 200π or Distance covered in 1 sec = 200π/40 = 5π

∴ Distance covered in 140 seconds = 140 $\times$ 5π

➭ 700π

➭ 700 $\times$ 22/7

➭ 100 $\times$ 22

➭ 2200 m

Hence, Distance covered at the end is 2200 m.

[ Now, Displacement ]

• It is given that athelete take 40 sec to cover one round and he ram for 220 seconds.

∴ Total rounds = Total distance covered/Distance covered in one round

➨ 700π/200π

➨ 3.5 rounds.

Therefore, if he started from point A after 140 seconds he will be at point B.

Hence, Displacement = Point A to B

➨ 100 + 100

➨ 200 m.