Question

an athletic complete one round of a circular track of 40s. what will be the distance covered and displacement at the end of 2 min and 20s​

Answer 1

Correct Question

An athletic complete one round of a circular track of radius R in 40s. what will be the distance covered and displacement at the end of 2 min and 20s?

Solution-

An athlete completes one round of a circular track having radius 'R' in 40 seconds.

We have to find the distance and displacement of the athele at the end of 2 min 20 sec.

Distance is defined as the total path covered by the body. Whereas displacement is defined as the shortest path covered between the initial and final points.

First of all convert the given time into seconds. (2 min 20 sec)

= 2 × 60 sec + 20 sec

= (120 + 20) sec

= 140 sec

Athele completes his one round in 40 sec. Then in 140 sec, he completes 3.5 rounds.

As,

40 sec = 1 round

140 sec = (1 × 140)/40 = 3.5 rounds

Distance covered = 3.5 × Circumference of circle

= 3.5 × 2πr

= 3.5 × 2 × 22/7 × R

= 22R m

Also, in 3.5 rounds; athlete will be just at the opposite side of the circular track. Means, equal to the diameter of the circular track.

2 × Radius = Diameter

2 × R = Diameter

Therefore, the distance covered is 22R m and displacement of the athele at the end of 2 min 20 sec is 2R.

Answer 2

Correct 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 the end 2 min 20s

Given:

• Time taken to complete one round of a circular track = 40s
• Diameter = 200m

To find:

• Distance and displacement at time of 2min 20s

Conversion:

2min 20s → seconds

2min 20s → 120s + 20s

2min 20s → 140s

Solution:

Firstly finding radius

2(radius) = Diameter

♦ 200 = 2r

♦ r = 200/2

♦ r = 100

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Circumference of 3.5 rounds = Distance travelled in 140s

Because , ↓

Here, for 40s the athletic completes 1 round for 140s =

In other form

40s → 1 round

140s → ? rounds be x

Cross multiplying we have

→ 40x = 140

→ x = 140/40 = 7/2

→ x = 3.5

For 140s the athletic completes 3.5 rounds

Now,

Distance travelled in 140s = 3.5 × 2πr

Distance travelled = 7πr

Distance travelled = 7(22/7)(100)

Distance travelled = 2200

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Displacement = 3.5 × diameter

Displacement = 7/2 × 200

Displacement = 700

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Hence , distance & displacement travelled in 2min 20s is 2200m & 700m