Question

An athlete completes one round of a circular track of diameter 200m in 40s .what will be the Distance covered and the displacement at end of 2minutes 20seconds​

Answer 1

Answer:

Given, Total time = 2 minutes 20 seconds

= 2 × 60 + 20 (As 1 Minute= 60 Seconds)

= 120 + 20

= 140 seconds

According to Question,

In 40 Seconds⇒ 1 Round is completed

∴In 140 Seconds⇒

(a) Calculation of Distance Covered in

3.5 Rounds

Diameter of circular track = 200m (Given)

∴Radius of circular track, (r) = 100m( Diameter/2)

Now, Distance covered in 1 round = Circumference of the circular track

= 2πr

=2*22/7*100

= 628.57 m

∴ Distance covered in 3.5 Rounds = 628.57 X 3.5= 2200 m

(b) As the athlete makes 3.5 rounds of the circular track, Suppose he starts from point A then after completing the 3 rounds he will be at the same point A. On starting again from the same point(Point A) and makes the remaining half round then he will reach at the point B. Therefore, the displacement of the athlete will be equal to the diameter of the track i.e., 200m.

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Answer 2

Answer:

Distance covered in 2 m 20 s = 2198 m

And, displacement after 2 m 20 s = 200m

Explanation:

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

Time of one rotation = 40s

Time after 2m20s = (2 x 60s + 20s) = 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, rotating in 40 s=1

Therefore, rotation in

1s=140

∴ 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