The length of path covered by a moving body between its initial and final positions is called the distance covered by the body. Distance is a scalar quantity, and its SI unit is meter. Distance always increases with time.

An athlete completes one round of a circular track of diameter 49 m in 20 s . Calculate the distance covered and displacement at the end of 30 s .

Given that, Diameter of the track, D = 49 m Time taken for one cycle, T = 20 s Total time taken by the athlete, t = 30 s Total rounds completed in 30 s is, n = t T = 30 20 = 1 . 5 We know that the distance per one round is equal to the circumference of a circle which is equal to πD . Thus, the total distance travelled (let it be x ) in 30 s is, x = nπD = 3 πD 2 = 3 2 × 22 7 × 49 = 231 m After completing one and half round, the athlete will be at the exact opposite point of the circle. That is, the displacement will be equal to the diameter which is 49 m .

An athlete completes one round of a circular track of diameter 200 m in 40 s . What will be the distance covered and the displacement at the end of 2 m i n 20 s ?

Given that diameter of the circular track, d = 200 m The radius of the track, r = d 2 = 100 m Time of running, t = 2 min 20 s = 140 s We know that circumference of a circular path is C = 2 π r = 2 π ( 100 ) = 200 π m And given that athlete completes one round in 40 s . In 40 s , athlete covers a distance of 200 π m . In unit time, the athlete will cover a distance = 200 π 40 m . The total distance covered by athlete in 140 s = 200 × 22 40 × 7 × 140 = 2200 m . When the athlete runs for 140 s , he completes 3 full round and a half-round around the circle. That means after 140 s he will be at a point which is diametrically opposite to the starting point. Therefore, the displacement will be equal to the diameter of the circular path which is 200 m .

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Distance can have positive and negative values.

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Important Questions on Motion

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Science>Physics>Motion>Distance and Displacement

An athlete completes one round of a circular track of radius

R

in 40 seconds. The displacement at the end of 2 minutes 20 seconds will be

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Science>Physics>Motion>Distance and Displacement

A car moving along straight line covers $\frac{1}{5} t h$ of total distance with speed $v_{1}$ and remaining part of distance with speed $v_{2}$ . The average velocity of car over entire distance is