Question

An athelete take 't' second to go once around a circular track of radius 'd'. what will be thr distance covet and velocity of the athelete? please explain​

Answer 1

According to the statement,

An athelete take 't' second to go once around a circular track of radius 'd'.

Provided that:

• Time = ‘t’ second
• Radius = ‘d’ metre

To determine:

• Distance covered
• Velocity of athlete

Solution:

• Distance covered = 2πd m
• Velocity of athlete = 2πd/t mps

Knowledge required:

⋆ In a circular track distance is equal to the circumference of the circle. It is given by the mentioned formula:

• ${\small{\underline{\boxed{\pmb{\sf{s \: = 2 \pi r}}}}}}$

Where, s denotes distance, π is pi, value of π can be taken as 22/7 or 3.14 and r denotes radius.

⋆ In a circular track the velocity is equal to the circumference/time. It is given by the mentioned formula:

• ${\small{\underline{\boxed{\pmb{\sf{v \: = \dfrac{2 \pi r}{t}}}}}}}$

Where, t denotes time.

Required solution:

~ Firstly let us calculate the distance travelled by using suitable formula!

$:\implies \rm Distance \: = Circumference \\ \\ :\implies \rm Distance \: = 2 \pi r \\ \\ :\implies \rm Distance \: = 2 \pi d \: metres \\ \\ {\pmb{\sf{Henceforth, \: solved!}}}$

~ Now let us calculate the velocity!

$:\implies \rm Velocity \: = \dfrac{Circumference}{Time} \\ \\ :\implies \rm v \: = \dfrac{2 \pi r}{t} \\ \\ :\implies \rm Velocity \: = \dfrac{2 \pi d}{t} \: ms^{-1} \\ \\ {\pmb{\sf{Henceforth, \: solved!}}}$