Question

An athlete completes one round of circular track of diameter 140m in 40 seconds. What will be the distance covered and the displacement at the end of 2 minutes 20 seconds

Answer 1

Given:

Diameter of Track, D= 140 m

Time taken by athlete to complete 1 round of track, t= 40 s

To Find:

​Distance covered and the displacement at the end of 2 min 20 s

Solution:

We know that,

• $\pink{\boxed{\bf{Radius=\frac{Diameter}{2}}}}$

• $\purple{\boxed{\bf{Circumference=2\pi r}}}$

where r is radius

• Distance is the length of actual path covered by body

• Displacement is the shortest distance between starting and final position

$\rule{190}{1}$

Given time t is

$\longrightarrow\rm{t=2\:min\:+20\:s}$

$\longrightarrow\rm{t=2\times60\:s\:+20\:s}$

$\longrightarrow\rm{t=120\:s\:+20\:s}$

$\longrightarrow\rm{t=140\:s}$

$\rule{190}{1}$

Now,

Rounds completed by athlete in 40s= 1

Rounds completed by athlete in 1s= $\rm{\dfrac{1}{40}}$

Rounds completed by athlete in 140s= $\rm{\dfrac{1}{40}\times140}$

or

Rounds completed by athlete in 140s= $\rm{3.5}$

That means athlete covers 3 and a half round in 140s

$\rule{190}{1}$

Let the radius of circular track be r

So,

$\longrightarrow\rm{r=\dfrac{D}{2}}$

$\longrightarrow\rm{r=\dfrac{140}{2}=70\:m}$

$\rule{190}{1}$

Let the circumference of circular track be C

So,

$\longrightarrow\rm{C=2\pi r}$

$\longrightarrow\rm{C=2\times\dfrac{22}{\cancel{7}}\times\cancel{70}}$

$\longrightarrow\rm{C=2\times22\times10}$

$\longrightarrow\rm{C=440\:m}$

$\rule{190}{1}$

Let the distance covered by athlete be d and displacement of athlete be d'

So,

$\longrightarrow\rm{d=3C+\dfrac{C}{2}}$

$\longrightarrow\rm{d=\dfrac{6C+C}{2}}$

$\longrightarrow\rm{d=\dfrac{7C}{2}}$

$\longrightarrow\rm{d=\dfrac{7\times440}{2}}$

$\longrightarrow\rm{d=\dfrac{3080}{2}}$

$\longrightarrow\rm\green{d=1540\:m}$

Also,

Since, after covering 3 and half rounds final position of athlete is diametrically opposite to starting position

Therefore,

$\longrightarrow\rm{d'=D}$

$\longrightarrow\rm\green{d'=140\:m}$

Hence, distance covered by athlete is 1540 m and displacement of athlete is 140 m.

Answer 2

$\bigstar$ Solution :

$\bigstar$ Given :

• Diameter of Track, D= 140 m
• Time taken by athlete to complete 1 round of track, t = 40 s

$\bigstar$ To Find :

• ​Distance covered and the displacement at the end of 2 min 20 s

$\bigstar$ Explanation :

$\star$ We know that,

$\star$ Diameter = 2 * Radius

• $Radius=\frac{Diameter}{2}$
• Circumference of circle , C = $2\pi r$

$\star$ where r is radius

• Distance is the length of actual path covered by body
• Displacement is the distance between starting and final position

$\star$ Given time t is given in minutes and seconds. But we need to convert it $\star$ to seconds.

=> t = 2 min + 20 sec

=> t = 2 * 60 sec + 20 sec

=> t = 120 sec + 20 sec

=> t = 140 sec

$\star$ Now,

$\star$ Rounds completed by athlete in 40 sec = 1

$\star$ Rounds completed by athlete in 1 sec = $\frac{1}{40}$

$\star$ Rounds completed by athlete in 140 sec= 140 * $\frac{1}{40}$

=> Rounds completed by athlete in 140 sec = 3.5

$\star$ That means athlete covers 3 and a half rounds in 140 sec

=> r = 140/2 = 70 m

$\star$ Let the circumference of circular track be C

=> C = $2\pi r$

=> C = 2 * 22/7 * 70

=> C = 440 m

$\star$ Let the distance covered by athlete be d and displacement of athlete be d'

$\star$ So,

=> d = 3 C + 0.5 C

=> d = 3 (440) + 0.5 (440)

=> d = 1320 + 220

=> d = 1540 m

$\star$ But displacement refers to difference of final and initial positions.

$\star$ Here half round is nothing but diameter of circular track.

$=>d^{'} =D\\\\=>d^{'}=140m$

                                                                                                 

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