Question

A cyclist moving along a circular path of radius 63 m completes three rounds in 3 minute. Calculate. 3M
The total distance covered by him during this time.
Net displacement of the cyclist.
The speed of the cyclist.

Answer 1

Concept:

Speed is distance travelled in per unit time, and displacement is the shortest distance between initial and final position.

Given:

Radius of circular track = 63 m

Completed 3 rounds in 3 minutes

Find:

Total distance covered by him.

Net displacement of the cyclist.

Speed of the cyclist.

Solution:

Distance in 1 round = perimeter of the round

Distance in 1 round = 2πr

where r is radius and which is given as 63 m

Distance in 1 round = 2×3.14×63 m

Distance in 1 round = 395.64 m

Distance in 3 round = 3 × 395.64 m

Distance in 3 round = 1186.92 m

As the initial and final position is same after 3 rounds than the shortest distance will be 0, Hence the displacement will be zero.

Speed = Distance / Time

Distance = 1186.92 m

Time = 3 Minutes or 180 seconds

Speed = ( 1186.92 / 180 ) m/s

Speed = 6.59 m/s

Hence, The total distance and displacement travelled by cyclist will be 1186.92 m and 0 m respectively. Moreover the speed will be 6.59 m/s.

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Answer 2

Answer:

The distance covered by him during this time is 1188.

The net displacement of the cyclist is 0.

The speed of the cyclist is $6.6$ m/s.

Explanation:

Given:-

The radius of the circular path, r = 63 m

Time taken to complete 3 rounds = 3 minutes

                                                        = 3 × 60 seconds

                                                        = 180 seconds

(a) Find the total distance covered by him during this time.

The distance covered by him in one round = Circumference of the circle

                                                                       = 2$\pi$r

                                                                       = $2\times \frac{22}{7}\times 63$

                                                                       = $2\times 22\times 9$

                                                                       = 396 m

Thus, the distance covered by him in three rounds = 3 × 396

                                                                                      = 1188 m

(b) Find the net displacement of the cyclist.

The shortest path between the initial and the final position is known as the displacement.

Since after 3 rounds, the final and the initial position is same.

Thus, the net displacement of the cyclist is 0.

(c) Find the speed of the cyclist.

Speed = (Distance covered by him in 3 rounds) / (Time taken to complete 3 rounds)

= 1188/180

= 6.6 m/s.

Therefore, the speed of the cyclist is $6.6$ m/s.

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