Question

derive equations of motion from newton's second law​

Answer 1

Answer:

In equation form, Newton's second law of motion is a=Fnetm a = F net m . ... The weight w of an object is defined as the force of gravity acting on an object of mass m. The object experiences an acceleration due to gravity g: w = mg.

Answer 2

ɴᴇᴡᴛᴏɴ’s sᴇᴄᴏɴᴅ ʟᴀᴡ sᴛᴀᴛᴇs ᴛʜᴀᴛ ᴛʜᴇ ᴀᴄᴄᴇʟᴇʀᴀᴛɪᴏɴ ᴏғ ᴀɴ ᴏʙᴊᴇᴄᴛ ᴅᴇᴘᴇɴᴅs ᴜᴘᴏɴ ᴛᴡᴏ ᴠᴀʀɪᴀʙʟᴇs – ᴛʜᴇ ɴᴇᴛ ғᴏʀᴄᴇ ᴀᴄᴛɪɴɢ ᴏɴ ᴛʜᴇ ᴏʙᴊᴇᴄᴛ ᴀɴᴅ ᴛʜᴇ ᴍᴀss ᴏғ ᴛʜᴇ ᴏʙᴊᴇᴄᴛ. ᴛʜᴇ ᴀᴄᴄᴇʟᴇʀᴀᴛɪᴏɴ ᴏғ ᴛʜᴇ ʙᴏᴅʏ ɪs ᴅɪʀᴇᴄᴛʟʏ ᴘʀᴏᴘᴏʀᴛɪᴏɴᴀʟ ᴛᴏ ᴛʜᴇ ɴᴇᴛ ғᴏʀᴄᴇ ᴀᴄᴛɪɴɢ ᴏɴ ᴛʜᴇ ʙᴏᴅʏ ᴀɴᴅ ɪɴᴠᴇʀsᴇʟʏ ᴘʀᴏᴘᴏʀᴛɪᴏɴᴀʟ ᴛᴏ ᴛʜᴇ ᴍᴀss ᴏғ ᴛʜᴇ ʙᴏᴅʏ. ᴛʜɪs ᴍᴇᴀɴs ᴛʜᴀᴛ ᴀs ᴛʜᴇ ғᴏʀᴄᴇ ᴀᴄᴛɪɴɢ ᴜᴘᴏɴ ᴀɴ ᴏʙᴊᴇᴄᴛ ɪs ɪɴᴄʀᴇᴀsᴇᴅ, ᴛʜᴇ ᴀᴄᴄᴇʟᴇʀᴀᴛɪᴏɴ ᴏғ ᴛʜᴇ ᴏʙᴊᴇᴄᴛ ɪs ɪɴᴄʀᴇᴀsᴇᴅ. ʟɪᴋᴇᴡɪsᴇ, ᴀs ᴛʜᴇ ᴍᴀss ᴏғ ᴀɴ ᴏʙᴊᴇᴄᴛ ɪs ɪɴᴄʀᴇᴀsᴇᴅ, ᴛʜᴇ ᴀᴄᴄᴇʟᴇʀᴀᴛɪᴏɴ ᴏғ ᴛʜᴇ ᴏʙᴊᴇᴄᴛ ɪs ᴅᴇᴄʀᴇᴀsᴇᴅ.

ᴀᴄᴄᴇʟᴇʀᴀᴛɪᴏɴ ɪs ᴅɪʀᴇᴄᴛʟʏ ᴘʀᴏᴘᴏʀᴛɪᴏɴᴀʟ ᴛᴏ ᴛʜᴇ ɴᴇᴛ ғᴏʀᴄᴇ ᴀɴᴅ ɪɴᴠᴇʀsᴇʟʏ ᴘʀᴏᴘᴏʀᴛɪᴏɴᴀʟ ᴛᴏ ᴛʜᴇ ᴍᴀss.

ɴᴇᴡᴛᴏɴ’s sᴇᴄᴏɴᴅ ʟᴀᴡ ᴄᴀɴ ʙᴇ ғᴏʀᴍᴀʟʟʏ sᴛᴀᴛᴇᴅ ᴀs,

ᴛʜᴇ ᴀᴄᴄᴇʟᴇʀᴀᴛɪᴏɴ ᴏғ ᴀɴ ᴏʙᴊᴇᴄᴛ ᴀs ᴘʀᴏᴅᴜᴄᴇᴅ ʙʏ ᴀ ɴᴇᴛ ғᴏʀᴄᴇ ɪs ᴅɪʀᴇᴄᴛʟʏ ᴘʀᴏᴘᴏʀᴛɪᴏɴᴀʟ ᴛᴏ ᴛʜᴇ ᴍᴀɢɴɪᴛᴜᴅᴇ ᴏғ ᴛʜᴇ ɴᴇᴛ ғᴏʀᴄᴇ, ɪɴ ᴛʜᴇ sᴀᴍᴇ ᴅɪʀᴇᴄᴛɪᴏɴ ᴀs ᴛʜᴇ ɴᴇᴛ ғᴏʀᴄᴇ, ᴀɴᴅ ɪɴᴠᴇʀsᴇʟʏ ᴘʀᴏᴘᴏʀᴛɪᴏɴᴀʟ ᴛᴏ ᴛʜᴇ ᴍᴀss ᴏғ ᴛʜᴇ ᴏʙᴊᴇᴄᴛ.

ᴛʜɪs sᴛᴀᴛᴇᴍᴇɴᴛ ɪs ᴇxᴘʀᴇssᴇᴅ ɪɴ ᴇǫᴜᴀᴛɪᴏɴ ғᴏʀᴍ ᴀs,

ᴀ=ғɴᴇᴛᴍ ᴛʜᴇ ᴀʙᴏᴠᴇ ᴇǫᴜᴀᴛɪᴏɴ ᴄᴀɴ ʙᴇ ʀᴇᴀʀʀᴀɴɢᴇᴅ ᴛᴏ ᴀ ғᴀᴍɪʟɪᴀʀ ғᴏʀᴍ ᴀs

ғ=ᴍᴀ sɪɴᴄᴇ ғᴏʀᴄᴇ ɪs ᴀ ᴠᴇᴄᴛᴏʀ, ɴᴇᴡᴛᴏɴ’s sᴇᴄᴏɴᴅ ʟᴀᴡ ᴄᴀɴ ʙᴇ ᴡʀɪᴛᴛᴇɴ ᴀs

ғ⃗ =ᴍᴀ⃗ ᴛʜᴇ ᴇǫᴜᴀᴛɪᴏɴ sʜᴏᴡs ᴛʜᴀᴛ ᴛʜᴇ ᴅɪʀᴇᴄᴛɪᴏɴ ᴏғ ᴛʜᴇ ᴛᴏᴛᴀʟ ᴀᴄᴄᴇʟᴇʀᴀᴛɪᴏɴ ᴠᴇᴄᴛᴏʀ ᴘᴏɪɴᴛs ɪɴ ᴛʜᴇ sᴀᴍᴇ ᴅɪʀᴇᴄᴛɪᴏɴ ᴀs ᴛʜᴇ ɴᴇᴛ ғᴏʀᴄᴇ ᴠᴇᴄᴛᴏʀ.