Question

an athlete completes one athlete completes one round of a circular track of diameter 200 metre in 40 seconds what will be the distance covered and the displacement at the end of the two minutes 20 seconds ​

Answer 1

Explanation:

Here we have, 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 a circular path

=

Circumference

time

⇒ v = 2πr/40s

⇒ v = 2 × 3.14 × 100m/ 40s

⇒ v = 628m/40s

⇒ v = 15.7m/s

(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 1/40s

= 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

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