Question

answer it with steps.​

Answer 1

Answer:

(i). Distance = 314 m

Displacement = 200 m

(ii). Distance = 628 m

Displacement = 0 m

Note:

★ Distance : The actual length travelled by the body is called distance .

★ Displacement : The shortest length between the initial point and the final point of the body is called displacement .

★ Distance ≥ Displacement

★ Diameter of circle = 2×Radius

★ Circumference of circle = 2π×Radius

★ Semi-Circumference = π×Radius

Solution:

Given: Radius , r = 100 m

To find : Distance and displacement after half round and complete round.

(i). For half round :

★ Distance = Actual path length

Here,

The actual path length travelled by man is the arcAB .

Thus,

Distance = arcAB

= Semi-Circumference

= π×Radius

= π×100

= 100π m

OR

= 100×3.14 m

= 314 m

★ Displacement = Shortest path

Here,

A is the initial point and B is the final point of the man .

Thus,

The shortest length between the initial point A and final point B is diameter AB .

Thus,

Displacement = diameter AB

= 2×Radius

= 2×100

= 200 m

Hence,

Distance = 314 m

Displacement = 200 m

°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°

(ii). For complete round :

★ Distance = Actual path length

Here,

The actual path length travelled by man is the circumference of the circular track .

Thus,

Distance = Circumference

= 2π×Radius

= 2π×100

= 200π m

OR

= 200×3.14 m

= 628 m

★ Displacement = Shortest path

Here,

A is the initial point and A is the final point of the man .

Thus,

The shortest length between the initial point A and final point A is zero.

Thus,

Displacement = 0

Hence,

Distance = 628 m

Displacement = 0 m

Answer 2

ᴀᴄᴛᴜᴀʟ ǫᴜᴇsᴛɪᴏɴ:-

A man is walking on a circular track of radius 100 m. Calculate the distance and displacement in:-

1. Half round,
2. One complete round.

ᴘᴀɴᴛʜᴇʀɪᴏ's ʀᴇsᴘᴏɴsᴇ:-

ᴋɴᴏᴡʟᴇᴅɢᴇ sᴄᴀʀ:-

• Distance: Length of the actual path.
• Displacement: Shortest length between the initial and the final position of a body.

Actual Content:-

1.

While half round,

Distance = $\sf{\frac{2πr}{2}}$

or, $\sf{πr}$

or, $\sf{100π}$ metres.

or, $\sf{≈ 314}$ metres.

Displacement = $\sf{100 × 2}$ metres

or, $\sf{200}$ metres

2.

While a complete round,

Distance = $\sf{2πr}$

or, $\sf{2π(100)}$ metres

or, $\sf{200π}$ metres

or, $\sf{≈ 628}$ metres.

Displacement = $\sf{0}$ metres.

[Why? 'Cause the initial and the final positions have coincided with each other].