Question

An athlete completes one round of a square track whose area is 400 sq.

meter in 45 s. What will be the distance covered, Average speed and the

displacement at the end of 2 minutes 15 s?​

Answer 1

Given :-

Area of the circular track = 400 m

Time taken to complete one round = 45 sec

To Find :-

The average speed.

The displacement at the end of 2 min 15 sec.

Analysis :-

Firstly find the number of rounds completed by the athlete accordingly.

Then the total distance covered accordingly.

Finally to find the average speed, substitute the values accordingly such that speed is equal to total distance divided by time taken.

Solution :-

We know that,

• s = Side
• a = Area
• t = Time
• p = Perimeter
• d = Displacement
• v = Speed

Finding the number of rounds,

Given that,

Time (t) = 2 min 15 sec = 135 sec

Time taken to complete one round = 45

Substituting their values,

⇒ 135/45

⇒ 3 rounds

Using the formula,

$\underline{\boxed{\sf Area \ of \ a \ square=Side \times Side}}$

Given that,

Area (a) = 400 m²

Substituting their values,

⇒ s × s = 400

⇒ s² = 400

⇒ s = √400

⇒ s = 20 m

Using the formula,

$\underline{\boxed{\sf Perimeter \ of \ a \ square=4 \times Side}}$

Given that,

Side (s) = 20 m

Substituting their values,

⇒ p = 4s

⇒ p = 4 × 20

⇒ p = 80 m

Number of rounds = 3

⇒ 3 × 80

⇒ 240 m

Using the formula,

$\underline{\boxed{\sf Average \ speed=\dfrac{Total \ displacement}{Time \ taken} }}$

Given that,

Distance (s) = 240 m

Time (t) = 45 sec

Substituting their values,

⇒ s = d/t

⇒ s = 240/45

⇒ s = 5.33 m/s

Therefore,

Average speed = 5.33 m/s

Distance at the end of 2 min 15 sec = 240 m

Answer 2

Answer:

Given :-

• Area of square track = 400 m²
• Time taken to cover = 45 s

To Find :-

Distance covered, Average speed and the displacement at the end of 2 minutes 15 s?

Solution :-

Firstly let's found total round covered

135/4 = 33.75 rounds

$\boxed{ \bf \: circumference = 2\pi r}$

Radius = Diameter/2

Radius = 400/2

Radius = 200 cm

Now,

33.75 × 2 × 22/7 × 200

67.5 × 22 × 100 / 7

67.5 × 2200 / 7

148500 / 7

21214.2 m

Average speed = Total Displacement/Time taken

Average speed = 21214.2/45

Average speed = 157.14 m/s