Question

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

Answer 1

Answer:

Distance = 2198 m

Displacement = 200 m

Explanation:

Given,

Diameter = 200 m. Then, radius = 100 m.

Time of one rotation = 40 seconds.

Time after 2 minutes 20 seconds = 140 seconds.

Now,

We know that, Velocity = (Circumference/Time)

v = (2πr)/40

⇒ v = (2 * 3.14 * 100)/40

⇒ v = (628)/40

⇒ v = 15.7 m/s

(i) Distance after 2 minutes 20 seconds :

We know that, Distance = velocity * Time

⇒ Distance = 15.7 * 140

⇒ Distance = 2198 m

(ii) Displacement after 2 minutes 20 seconds :

Given that,

40 seconds = 1 round

rotation in 1 second = (1/40)

Then,

∴ Rotation in 140 seconds = (1/4) * 140 = 3.5

So, the athlete completes 3.5 rounds.

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.

Thus,

His displacement = Diameter of circular track = 200 m

Therefore,

Displacement after 2 min 20 sec = 200 m.

Hope it helps!

Answer 2

Answer:

An athlete takes 40 sec for 200 m diameter circular track.

It means he covers 2 pi R distance (2R = 200 m) in 40 sec,

Then,

In 2 min 20 sec=140 sec, he moves{2 pi R)/40} x140 = 7 pi R

Therefore the total distance travelled is given by

d = 7 pi R

= 7 x(22/7)x100

= 2200m

displacement = Shortest path travelled by any object.

So after 7 pi R it'll be at point diametrically opposite point of its initial position.

then displacement = 2R =200m.