Question

An athelete completes one round of a circular track of dia diameter 200 m in 40 s . what will be the distance covered and the displacement at the end of 2min 20 s

Answer 1

Answer:

The athlete covers the revolution around 200 m diameter circle in 40 seconds.

So the circumference be d

$d = 2\pi r$

$= > d = 2\pi (\dfrac{200}{2} )$

$= > d = 200\pi \: metres$

So we are observing a time of 2 minutes + 20 seconds ( i.e 140 seconds ) , the body will make 3 full revolutions in 120 seconds and ½ revolutions in 20 seconds.

So total distance travelled will be 3½ revolutions.

$distance = 3 \frac{1}{2} (d)$

$= > distance = \frac{7}{2} (200\pi)$

$\boxed{ \bold{= > distance = 700\pi \: metres}}$

Displacement will be simply the length of diameter.

$\boxed{ \bold{displacement = diameter = 200 \: m}}$

Answer 2

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❚ QuEstiOn ❚

# An athelete completes one round of a circular track of dia diameter 200 m in 40 s . what will be the distance covered and the displacement at the end of 2min 20 s = ?

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❚ ANsWeR ❚

✺ Given :

• diameter = 200 m
• Total time taken for 1 revolution = 40 sec.

✺ To FinD :

• distance covered and the displacement at the end of 2min 20 s .

✺ Figure :

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$\setlength{\unitlength}{1 cm}\begin{picture}(12,6)\thicklines\put(7.5,7.5){\circle{4}}\put(7.4,7.6){ d }\put(6.8,7.5){\line(1,0){1.4}}\put(8.7,7.6){ d=200\:m }\put(4.5,7.6){ . }\end{picture}$

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✺ Explanation :

$\therefore\:\: Circumference=\pi d$

$\therefore\:\: Circumference=200\pi\:m$

Now , 2min 20 s = (120+20) sec= 140 sec

• Time taken for 1 revolution = 40 sec.

∴ in 120 sec it will revolute = $\dfrac{\cancel{120}}{\cancel{40}}$ = 3 times.

and in remaining 20 seconds the athelete will complete = $\dfrac{\cancel{20}}{\cancel{40}}$ = $\dfrac{1}{2}$ times.

∴ Total revolution = 3.5 times

✏ So the total distance covered by the athelete will be = 3.5 × Circumference = 700π meters.

Now , the displacement of the athelete will be the length of the diameter

( cuz for a half revolution the displacement between the starting and the end points will simply be diameter of the circular track .)

[ we also know that for a complete revolution the the displacement is zero cuz the starting and the end points are same so displacement = 0

so , the first 3 revolution will not take into account . ]

✏ The displacement = Diameter = 200 m

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