Question

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An athelet completes one round of a circular trake of diameter 200 m in a 40 sec. What will be the distance covered and the displacement at the end of 2 mins 20 sec.

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Answer 1

To find distance and Displacement
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Diameter of circular track = 200 m

so,perimeter of the circular track will be

= 2×pi×r=200×pi = 200× 22/7 m

= 4400/7 m

= 628.5 m

so He cover a distance of 20(pi) m in 40 sec.

hence,
Speed =( 200 × pi)/40

=5 (pi)


Now,

Distance covered and displacement after 2 minute 20 seconds.

so, time in seconds =(60×2)+20

: = 140 sec

speed= 5 (pi) m/sec
=5× 22/7m/sec
=110/7 m/sec

so,
Distance distance travel =Speed × time

=(110/7)×140 m

= 110×20 m

= 2200 m
so,
on dividing = 2200/(4400/7)

= (2200/4400)× 7

= 1/2×7 =7/2 = 3.5

So ,
here it is taking 3 Revolution and one- half revolution.

so, Displacement = 1/2 of Parameter of circule

= 1/2 × 628.5 m

= 314.25 m

so, 314.25 m will be the displacement.

Answer 2

Hey mate!

Here's your answer!!

Given that ,
Diameter = 200 m, therefore,
radius = 200m/2 = 100 m

Time of one rotation = 40s
Time after 2m20s = 2 x 60s + 20s = 140s
Distance after 140 s = ?
Displacement after 140s =?
-------------------------
We know that velocity along circular path,


$v = \frac{circumference}{time}$
$v = \frac{2\pi \: r}{40s}$
$v = \frac{2 \times 3.14 \times 100m}{40s}$
$v = \frac{628m}{40s}$
$v = 17.5mtr \: per \: sec$
a) Distance after 140s

We know that,distance=velocity ×time

⇒ distance=15.7m/s ×140 s = 2198 m

(b) Displacement after 2 m 20 s i.e. in 140 s

Since,rotatin in 40 s=1

Therefore, rotation in 1s = 1/40

Rotation in 140s = 1/40 × 140 = 3.5

Therefore, in 3.5 rotations athlete will be just at the opposite side of the circular track, i.e. at a distance equal to the diameter of the circular track which is equal to 200 m.

Therefore,
Distance covered in 2 m 20 s = 2198 m

And, displacement after 2 m 20 s = 200m.

Hope it helps you!!!
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