Question

A cyclist completes one round of circular track of radius 20m in 20 seconds What will be the displacement at the end of 20s and 30s?

Answer 1

Answer:

0 m & 40 m

Explanation:

As per the provided information in the given question, we have :

• A cyclist completes one round of circular track of radius 20 m in 20 seconds.

We've been asked to calculate his displacement at the end of 20 s and 30 s.

⠀⠀⠀⠀⠀⠀⠀⠀» Suppose that the cyclist starts from point A. Now, we'll find the displacement at the end of 20s and 30s, for that we'll need his final and initial position in both case, at the end of 20s and 30s. In both cases the initial position is A.

$\large {\underline { \sf {Displacement \; at \; the \; end \; of \; 20s :}}}$

Here, the the initial position is A. According to the question, he completes one round of circular track of radius 20 m in 20 seconds. This statement implies that at the end of 20 seconds it'll again come back to point A.

As the body comes back to its initial position after covering certain distance, so his displacement at the end of 20 seconds will be 0.

$\large {\underline { \sf {Displacement \; at \; the \; end \; of \; 30s :}}}$

Basically, here is also his initial position is A. Now, we need to find his position at the end of 30s. For that, we'll find the rounds covered by him in 30s.

In 20 s is covers 1 round. So, in 1 second it'll cover 1 second it covers 1/20 rounds. If it covers 1/20 rounds in 1 second. So,

$\dashrightarrow \quad \rm { Rounds_{(30s)} = \dfrac{1}{20} \times 30 \; rounds }$

Performing multiplication.

$\dashrightarrow \quad \rm { Rounds_{(30s)} = \cancel{\dfrac{30}{20}} \; rounds }$

Cancel the terms.

$\dashrightarrow \quad \underline{\boxed{\rm { Rounds_{(30s)} = 1.5 \; rounds }}}$

Therefore, in 30 s it'll cover 1.5 rounds which is equal to 1 + 0.5 rounds or 1 + Half round. After 1 round it'll again come back to point A. Then in order to complete 0.5 rounds more it'll cover half of the total path of the track and will come to point B. (Refer to the attachment 2.) Point B is his final position.

As the displacement is the shortest distance from initial to final position, thus here shortest distance from point A to B will be a straight line that is the diameter of the circular path. Let us denote displacement as S.

$\dashrightarrow \quad \rm { S = Diameter}$

$\dashrightarrow \quad \rm { S = 2 \times Radius}$

We've been given that the radius of the track is 20 m. So,

$\dashrightarrow \quad \rm { S = 2 \times 20 \; m}$

$\dashrightarrow \quad \underline{\boxed{\bf { S = 40 \; m}}}$

∴ The displacement at the end of 20s is 0 m and at the end of 30s is 40 m.

$\rule{200}2$