Question

A cyclist goes around a circular track once every 2 minutes. If the radius of the
circular track is 105 metres, calculate his speed.​

Answer 1

Given :-

Radius of circular track = 105 m

Time taken by the cyclist = 2 min

To Find :-

The speed of the cyclist.

Analysis :-

Here we are given with the radius and the time taken by the cyclist.

Firstly, we've to find the distance covered by the cyclist so substitute the values in the question in it's respective formula.

In order to find the speed, substitute the values accordingly such that speed is equal to distance divided by time taken.

Solution :-

We know that,

• s = Speed
• d = Distance
• t = Time
• r = Radius
• c = Circumference

Using the formula,

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

Given that,

Radius (r) = 105 m

Substituting their values,

⇒ c = 2 × (22/7) × 105

⇒ c = (2 × 22 × 105) / 7

⇒ c = 4620 / 7

⇒ c = 660 m

Using the formula,

$\underline{\boxed{\sf Speed= \dfrac{Total \ distance}{Total \ time} }}$

Given that,

Distance (d) = 660 m

Time (t) = 2 min = 120 sec

Substituting their values,

⇒ s = d/t

⇒ s = 660/120

⇒ s = 5.5 m/s

Therefore, the speed of the cyclist is 5.5 m/s.