Question

Derive Newton's 1st Law from 2nd Law​

Answer 1

ɴᴇᴡᴛᴏɴ's ғɪʀsᴛ ʟᴀᴡ sᴛᴀᴛᴇs ᴛʜᴀᴛ ᴀ ʙᴏᴅʏ sᴛᴀʏs ᴀᴛ ʀᴇsᴛ ɪғ ɪᴛ ɪs ᴀᴛ ʀᴇsᴛ ᴀɴᴅ ᴍᴏᴠᴇs ᴡɪᴛʜ ᴀ ᴄᴏɴsᴛᴀɴᴛ ᴠᴇʟᴏᴄɪᴛʏ ᴜɴɪᴛ ɪғ ᴀ ɴᴇᴛ ғᴏʀᴄᴇ ɪs ᴀᴘᴘʟɪᴇᴅ ᴏɴ ɪᴛ. ɴᴇᴡᴛᴏɴ's sᴇᴄᴏɴᴅ ʟᴀᴡ sᴛᴀᴛᴇs ᴛʜᴀᴛ ᴛʜᴇ ɴᴇᴛ ғᴏʀᴄᴇ ᴀᴘᴘʟɪᴇᴅ ᴏɴ ᴛʜᴇ ʙᴏᴅʏ ɪs ᴇǫᴜᴀʟ ᴛᴏ ᴛʜᴇ ʀᴀᴛᴇ ᴏғ ᴄʜᴀɴɢᴇ ɪɴ ɪᴛs ᴍᴏᴍᴇɴᴛᴜᴍ.

Answer 2

First Law of motion :-

A body at rest will remain at rest,and a body in motion will continue in motion in a straight line with a uniform speed, unless it is compelled by an external force to change its state of rest or of uniform motion.

Second Law of motion :-

It states that the rate of change of momentum is directly proportional to the force applied.

→ Force = Mass × Acceleration

Or,

→ F = ma

→ F = m × (v - u)/t .....(i)

As we know that,

• a = v - u/t

If there is no force applied,

→ F = 0

From equation i) :-

→ 0 = m × (v - u)/t

→ v - u/t = 0

→ v - u = 0

→ v = u ....(ii)

→ Final velocity = Initial velocity

If initially the body is at rest,

→ u = 0

From equation ii)

→ v = u × 0

→ v = 0 ....(iii)

From equation (ii) and (iii) it is proved that first law of motion lies in second law of motion.

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