Question

Derive three equations of motion graphically.
(please answer)​

Answer 1

Answer:

first equation of motion u =v+at

second equation of motion s =ut+1/2 at2

third equation of motion v2 =u2+2as.

here is impossible to draw the graphic method.

Answer 2

ғɪʀsᴛ

ɪɴ ᴛʜᴇ ᴀʙᴏᴠᴇ ɢʀᴀᴘʜ,

ᴛʜᴇ ᴠᴇʟᴏᴄɪᴛʏ ᴏғ ᴛʜᴇ ʙᴏᴅʏ ᴄʜᴀɴɢᴇs ғʀᴏᴍ ᴀ ᴛᴏ ʙ ɪɴ ᴛɪᴍᴇ ᴛ ᴀᴛ ᴀ ᴜɴɪғᴏʀᴍ ʀᴀᴛᴇ.

ʙᴄ ɪs ᴛʜᴇ ғɪɴᴀʟ ᴠᴇʟᴏᴄɪᴛʏ ᴀɴᴅ ᴏᴄ ɪs ᴛʜᴇ ᴛᴏᴛᴀʟ ᴛɪᴍᴇ ᴛ.

ᴀ ᴘᴇʀᴘᴇɴᴅɪᴄᴜʟᴀʀ ɪs ᴅʀᴀᴡɴ ғʀᴏᴍ ʙ ᴛᴏ ᴏᴄ, ᴀ ᴘᴀʀᴀʟʟᴇʟ ʟɪɴᴇ ɪs ᴅʀᴀᴡɴ ғʀᴏᴍ ᴀ ᴛᴏ ᴅ, ᴀɴᴅ ᴀɴᴏᴛʜᴇʀ ᴘᴇʀᴘᴇɴᴅɪᴄᴜʟᴀʀ ɪs ᴅʀᴀᴡɴ ғʀᴏᴍ ʙ ᴛᴏ ᴏᴇ (ʀᴇᴘʀᴇsᴇɴᴛᴇᴅ ʙʏ ᴅᴏᴛᴛᴇᴅ ʟɪɴᴇs).

ғᴏʟʟᴏᴡɪɴɢ ᴅᴇᴛᴀɪʟs ᴀʀᴇ ᴏʙᴛᴀɪɴᴇᴅ ғʀᴏᴍ ᴛʜᴇ ɢʀᴀᴘʜ ᴀʙᴏᴠᴇ:

ᴛʜᴇ ɪɴɪᴛɪᴀʟ ᴠᴇʟᴏᴄɪᴛʏ ᴏғ ᴛʜᴇ ʙᴏᴅʏ, ᴜ = ᴏᴀ

ᴛʜᴇ ғɪɴᴀʟ ᴠᴇʟᴏᴄɪᴛʏ ᴏғ ᴛʜᴇ ʙᴏᴅʏ, ᴠ = ʙᴄ

ғʀᴏᴍ ᴛʜᴇ ɢʀᴀᴘʜ, ᴡᴇ ᴋɴᴏᴡ ᴛʜᴀᴛ

ʙᴄ = ʙᴅ + ᴅᴄ

ᴛʜᴇʀᴇғᴏʀᴇ, ᴠ = ʙᴅ + ᴅᴄ

ᴠ = ʙᴅ + ᴏᴀ (sɪɴᴄᴇ ᴅᴄ = ᴏᴀ)

ғɪɴᴀʟʟʏ,

ᴠ = ʙᴅ + ᴜ (sɪɴᴄᴇ ᴏᴀ = ᴜ) (ᴇǫᴜᴀᴛɪᴏɴ )

ɴᴏᴡ, sɪɴᴄᴇ ᴛʜᴇ sʟᴏᴘᴇ ᴏғ ᴀ ᴠᴇʟᴏᴄɪᴛʏ-ᴛɪᴍᴇ ɢʀᴀᴘʜ ɪs ᴇǫᴜᴀʟ ᴛᴏ ᴀᴄᴄᴇʟᴇʀᴀᴛɪᴏɴ ᴀ,

sᴏ,

ᴀ = sʟᴏᴘᴇ ᴏғ ʟɪɴᴇ ᴀʙ

ᴀ = ʙᴅ/ᴀᴅ

sɪɴᴄᴇ ᴀᴅ = ᴀᴄ = ᴛ, ᴛʜᴇ ᴀʙᴏᴠᴇ ᴇǫᴜᴀᴛɪᴏɴ ʙᴇᴄᴏᴍᴇs:

ʙᴅ = ᴀᴛ (ᴇǫᴜᴀᴛɪᴏɴ )

ɴᴏᴡ, ᴄᴏᴍʙɪɴɪɴɢ ᴇǫᴜᴀᴛɪᴏɴ & , ᴛʜᴇ ғᴏʟʟᴏᴡɪɴɢ ɪs ᴏʙᴛᴀɪɴᴇᴅ:

ᴠ = ᴜ + ᴀᴛ

sᴇᴄᴏɴᴅ

From the graph above, we can say that

Distance travelled (s) = Area of figure OABC = Area of rectangle OADC + Area of triangle ABD

s=(12AB×BD)+(OA×OC)

Since BD = EA, the above equation becomes

s=(12AB×EA)+(u×t)

As EA = at, the equation becomes

s=12×at×t+ut

On further simplification, the equation becomes

s=ut+12at2

ᴛʜɪʀᴅ

ғʀᴏᴍ ᴛʜᴇ ɢʀᴀᴘʜ, ᴡᴇ ᴄᴀɴ sᴀʏ ᴛʜᴀᴛ

ᴛʜᴇ ᴛᴏᴛᴀʟ ᴅɪsᴛᴀɴᴄᴇ ᴛʀᴀᴠᴇʟʟᴇᴅ, s ɪs ɢɪᴠᴇɴ ʙʏ ᴛʜᴇ ᴀʀᴇᴀ ᴏғ ᴛʀᴀᴘᴇᴢɪᴜᴍ ᴏᴀʙᴄ.

ʜᴇɴᴄᴇ,

s = ½ (sᴜᴍ ᴏғ ᴘᴀʀᴀʟʟᴇʟ sɪᴅᴇs) × ʜᴇɪɢʜᴛ

s=(ᴏᴀ+ᴄʙ)×ᴏᴄ

sɪɴᴄᴇ, ᴏᴀ = ᴜ, ᴄʙ = ᴠ, ᴀɴᴅ ᴏᴄ = ᴛ

ᴛʜᴇ ᴀʙᴏᴠᴇ ᴇǫᴜᴀᴛɪᴏɴ ʙᴇᴄᴏᴍᴇs

s= ½ (ᴜ+ᴠ) × ᴛ

ɴᴏᴡ, sɪɴᴄᴇ ᴛ = (ᴠ – ᴜ)/ ᴀ

ᴛʜᴇ ᴀʙᴏᴠᴇ ᴇǫᴜᴀᴛɪᴏɴ ᴄᴀɴ ʙᴇ ᴡʀɪᴛᴛᴇɴ ᴀs:

s= ½ ((ᴜ+ᴠ) × (ᴠ-ᴜ))/ᴀ

ʀᴇᴀʀʀᴀɴɢɪɴɢ ᴛʜᴇ ᴇǫᴜᴀᴛɪᴏɴ, ᴡᴇ ɢᴇᴛ

s= ½ (ᴠ+ᴜ) × (ᴠ-ᴜ)/ᴀ

s = (ᴠ-ᴜ)/ᴀ

ᴛʜɪʀᴅ ᴇǫᴜᴀᴛɪᴏɴ ᴏғ ᴍᴏᴛɪᴏɴ ɪs ᴏʙᴛᴀɪɴᴇᴅ ʙʏ sᴏʟᴠɪɴɢ ᴛʜᴇ ᴀʙᴏᴠᴇ ᴇǫᴜᴀᴛɪᴏɴ:

ᴠ = ᴜ+ᴀs