Question

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Answer 1

Question: An athlete complete one round of a circular track of diameter 200 metres in 40 seconds, what will be the distance cover and the displacement at the end of 2 minutes 20 seconds.

Provided that:

• Diameter of circle = 200 m
• Time taken = 40 seconds

To calculate:

• The distance at the end of 2 minutes 20 seconds.

• The displacement at the end of 2 minutes 20 seconds.

Solution:

• The distance at the end of 2 minutes 20 seconds = 2200 metres

• The displacement at the end of 2 minutes 20 seconds = 200 metres

Full solution:

~ Firstly let us calculate distance!

~ Firstly we have to convert minutes into seconds by applying suitable formula!

${\small{\underline{\boxed{\sf{1 \: minutes \: = 60 \: seconds}}}}}$

→ 1 minute = 60 seconds

→ 2 min = 2 × 60

→ 2 min = 120 seconds

→ 2 min 20 seconds = 120 + 20

→ 2 min 20 seconds = 140 seconds

~ Now let's convert diameter into radius by applying suitable formula!

${\small{\underline{\boxed{\sf{Radius \: = \dfrac{Diameter}{2}}}}}}$

$:\implies \sf Radius \: = \dfrac{Diameter}{2} \\ \\ :\implies \sf Radius \: = \dfrac{200}{2} \\ \\ :\implies \sf Radius \: = 100 \: metres$

~ Now let's ind out the number of rounds!

→ Rounds = Ending time/Starting time

→ Rounds = 140/40

→ Rounds = 3.5

~ Now let's find circumference of the circular track by using formula!

${\small{\underline{\boxed{\sf{Circumference \: = 2 \pi r}}}}}$

$:\implies \sf Circumference \: = 2 \pi r \\ \\ :\implies \sf Circumference \: = 2 \times \dfrac{22}{7} \times 100 \\ \\ :\implies \sf Circumference \: = \dfrac{44}{7} \times 100 \\ \\ :\implies \sf Circumference \: = \dfrac{4400}{7} \\ \\ :\implies \sf Circumference \: = 628.57 \: metres$

~ Now let's find distance by multiplying circumference with rounds

→ Distance = Circumference × Rounds

→ Distance = 628.57 × 3.5

→ Distance = 2200 metres

~ Now let's talk about displacement!

Explanation: Displacement is said to be the shortest distance. Therefore, according to figure the displacement is the diameter of the circular track itself!

→ Displacement = Diameter

→ 200 m = 200 m

→ Displacement = 200 m

Answer 2

Given parameters

The diameter of the circular track = 200m

Radius (r) = 200/2

r = 100m

Time t is taken by an athlete to complete one round = 40 second

Displacement = ??

Speed = Distance/Time

Total time athlete moves - 2min 20sec

2min 20sec = 2×60+20

2min 20sec = 140sec

Need to find the distance covered in one round

Distance covered in one round = Circumference of circle

Distance covered in one round = 2 pi r

Distance covered in one round = 2

Distance covered in one round = 2×100 pi

Distance covered in one round = 200 pi

Time is taken by an atthlete to complete one round = 40sec.

Number of rounds completed in 140sec = 140/40

Number of rounds completed in 140sec = 35

Distance covered = 3.5×circumference

Distance covered = 3.5×2 pi r

Distance covered = 3.5×2×3.14×100

Distance covered = 2200m

Hence, the distance covered at the end of 2min 20sec is 2200m or 22km.

And displacement is 200m as it returns to the initial position.