Question

An athlete covers 1 round in 20 s, what will be his distance and displacement 
at the end of 4.5 rounds? The radius of track is 100m.   ​

Answer 1

Answer:

His displacement is equal to the distance covered by him in 20 seconds. Note that this is the half of the time taken for a complete revolution, which suggests he has covered half the path, or is diagonally opposite to the initial point. Hence, after 3 minutes, his displacement is 200 m.

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Answer 2

Given,

• Radius of track = 100 m
• Time taken for one round = 20 sec

¤ To Find :

• Distance & Displacement at the end of 4.5 rounds.

We know,

• On a circular path, completion of one round, leads the gain of 0 metres of displacement & half round results in displacement of (2 × Radius of Path).

Now,

$\small \dag \:\:\text{Distance covered at the end of 4.5 rounds} \\ \bf \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \to2\pi r \times 4.5 \\ \bf \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \to9\pi r \\ \bf \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \to9 \times 3.14 \times 100 \\ \bf \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \to 9 \times \frac{314}{\cancel{100}} \times \cancel{100} \\ \\ \bf \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \to9 \times 314 = 2826 \: m \: \: \: \: \: \: \{ \tt{approx.}\}$

And,

$\bf{ \dag \: \: Displacement \: \: covered } \to 2 \times 100 \\ \bf \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \to200 \: m$

Hence,

• 2826 metres of distance is covered on completing 4.5 rounds of circular path with radius 100 m.
• 200 metres of displacement is made on taking 4.5 rounds of circular path having radius 100 m.

☆ Additional (#FAQs)

• Displacement is the shortest path between any two points.

▪ It is a vector quantity.

▪ Its SI Unit is metre.

▪ If between two points, both distance & displacement are to be figured out, The Displacement is always lesser than distance.

• Distance is measure of total length of path between certain points.

▪ It is scalar quantity.

▪ Its SI Unit is metre.

▪ Its formula is {Speed of object × Time taken}