Question

An athlete completes one round of a circular track of diameter 100m in 20s what will be the distance covered and the displacement in 40s​

Answer 1

Given:

Diameter of Track, D= 100 m

Time taken by athlete to complete 1 round of track, t= 20 s

To Find:

​Distance covered and the displacement at the end of 40 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

$\rule{190}{1}$

Rounds completed by athlete in 20s= 1

Rounds completed by athlete in 1s= $\dfrac{1}{20}$

Rounds completed by athlete in 40s= $\rm{\dfrac{1}{20}\times40}$

or

Rounds completed by athlete in 40s= 2

$\rule{190}{1}$

Let the radius of circular track be r

So,

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

$\longrightarrow\rm{r=\dfrac{100}{2}=50\:m}$

$\rule{190}{1}$

Let the circumference of circular track be C

So,

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

$\longrightarrow\rm{C=2\times\dfrac{22}{7}\times50}$

$\longrightarrow\rm{C=\dfrac{2200}{7}}$

$\longrightarrow\rm{C=314.28\:m}$

$\rule{190}{1}$

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

So,

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

$\longrightarrow\rm{d=2(314.28)}$

$\longrightarrow\rm\green{d=628.56\:m}$

Also,

Since, after covering 2 rounds athlete return to his starting position, so final position of athlete is same as the starting position

Therefore,

$\longrightarrow\rm\green{d'=0\:m}$

Hence, distance covered by athlete is 628.56 m and displacement of athlete is 0 m.