Give the dimensional formula of velocity.
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Dimensional formula of velocity is [LT¯¹].
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⠀⠀⠀ ❥ ❈ ᴅɪᴍᴇɴsɪᴏɴᴀʟ ғᴏʀᴍᴜʟᴀ ᴏғ ᴠᴇʟᴏᴄɪᴛʏ
ᴛʜᴇ ᴅɪᴍᴇɴsɪᴏɴᴀʟ ғᴏʀᴍᴜʟᴀ ᴏғ ᴠᴇʟᴏᴄɪᴛʏ ɪs ɢɪᴠᴇɴ ʙʏ,
ᴍ0 ʟ1 ᴛ-1
ᴡʜᴇʀᴇ,
ᴍ = ᴍᴀss
ʟ = ʟᴇɴɢᴛʜ
ᴛ = ᴛɪᴍᴇ
ᴅᴇʀɪᴠᴀᴛɪᴏɴ
ᴠᴇʟᴏᴄɪᴛʏ (ᴠ) = ᴅɪsᴘʟᴀᴄᴇᴍᴇɴᴛ × ᴛɪᴍᴇ-1 . . . . (1)
ᴛʜᴇ ᴅɪᴍᴇɴsɪᴏɴᴀʟ ғᴏʀᴍᴜʟᴀ ᴏғ ᴅɪsᴘʟᴀᴄᴇᴍᴇɴᴛ ᴀɴᴅ ᴛɪᴍᴇ ɪs [ᴍ0 ʟ1 ᴛ0] ᴀɴᴅ [ᴍ0 ʟ0 ᴛ1] ʀᴇsᴘᴇᴄᴛɪᴠᴇʟʏ . . . . (2)
ᴏɴ sᴜʙsᴛɪᴛᴜᴛɪɴɢ ᴇǫᴜᴀᴛɪᴏɴ (2) ɪɴ ᴇǫᴜᴀᴛɪᴏɴ (1) ᴡᴇ ɢᴇᴛ,
ᴠᴇʟᴏᴄɪᴛʏ = ᴅɪsᴘʟᴀᴄᴇᴍᴇɴᴛ × ᴛɪᴍᴇ-1
ᴏʀ, ᴠ = [ᴍ0 ʟ1 ᴛ-1]
ᴛʜᴇʀᴇғᴏʀᴇ, ᴠᴇʟᴏᴄɪᴛʏ ɪs ᴅɪᴍᴇɴsɪᴏɴᴀʟʟʏ ʀᴇᴘʀᴇsᴇɴᴛᴇᴅ ᴀs [ᴍ0 ʟ1 ᴛ-1].
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