Question

An athlete complete one round of a circular track of diameter 200 m in 40s . What will be the distance covered and the displacement at the end of 2 minutes 20s ?
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Answer 1

An athelete completes 1round of a circular track of diameter 200m in 40seconds. What will be the distance covered and the displacement at the end of 2minutes 20 seconds?

Answer :

Refer the attachment for the figure.

We know that, Displacement is the shortest distance between two points.

Now,

Circumference = 2 π r

Diameter = 200 m

Therefore, Radius = 100 m

Thus,

Distance covered in a round i.e 40 seconds = 2 × 22/7 × 100

=6.28×100

= 628 m

This is the distance covered in 40 sec.

Thus, Distance covered in 1 sec,

= 628/ 40

=15.7m

Now, As per your question,

We have to find the distance covered at the end of 2 min. 20 sec

2 min 20 sec = 140 sec.

Hence, Distance covered in 140 sec

= 15.7 × 140

= 2198 metres.

Distance covered in 140 sec is 2198 metres.

We know that, Displacement is the shortest distance between two points.

Displacement of the athlete will be equal to the diameter of the circular track.

∴ Displacement of the athlete = 200 m

Final answer :

The distance covered  is 2198 metres  the displacement at the end of 2 minutes 20 seconds is 200 m.

_______________________

Answer 2

$\mathfrak{\huge{Answer:}}$

$\mathbb{GIVEN}$

Diameter of the circular track = 200 m

Time taken to complete 1 round = 40 s

$\mathbb{TO\:FIND}$

The distance and the displacement after 2 minutes 20 seconds

$\mathbb{METHOD}$

Circumference of the track = $\sf{2 \pi r}$

Radius = $\sf{\frac{D}{2}}$

=》 Radius = $\sf{\frac{200}{2}}$

=》 Radius = 100 m

=》 Circumference = $\sf{200 \pi}$

Put the value of $\pi$

=》 $\sf{\frac{4400}{7}}$

Speed = $\frac{D}{T}$

Speed = $\frac{4400}{7} \times \frac{1}{40}$

Speed = $\sf{\frac{110}{7}}$m/s

Distance covered in 140 seconds ( 2 minutes 20 seconds = 120 + 20 seconds ) = Speed × Time

=》 $\sf{\frac{4400}{7}\times 140}$

Distance =》 $\boxed{\tt{2200\:m}}$

Number of rounds in 2200 m = $\sf{2200 \times \frac{7}{4400}}$

=》 $\boxed{\tt{3.5\:rounds}}$

Displacement after 3.5 rounds = 200m

Displacement after 2 minutes 20 seconds = 200 m

=》 $\boxed{\tt{200\:m}}$