A body covers one third of its journey with speed u next one thord with speed v and the last one third with speed w. calculate the average speed of the body during the entire journey
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ʜᴇʟʟᴏ ᴍᴀᴛᴇ!
ʟᴇᴛ ᴛᴏᴛᴀʟ ᴅɪsᴛᴀɴᴄᴇ ʙᴇ ᴅ
sᴘᴇᴇᴅ = ᴅɪsᴛᴀɴᴄᴇ / ᴛɪᴍᴇ
ᴜ = 1ᴅ/3 / ᴛ1
ᴛ1 = 1ᴅ/3ᴜ
ᴠ = 1ᴅ/3 / ᴛ2
ᴛ2 = 1ᴅ/3ᴠ
ᴡ = 1ᴅ/3 / ᴛ3
ᴛ3 = 1ᴅ/3ᴡ
ᴀᴠᴇʀᴀɢᴇ sᴘᴇᴇᴅ = ᴛᴏᴛᴀʟ ᴅɪsᴛᴀɴᴄᴇ / ᴛᴏᴛᴀʟ ᴛɪᴍᴇ
= ᴅ / ( 1ᴅ/3ᴜ + 1ᴅ/3ᴠ + 1ᴅ/3ᴡ )
= ᴅ / ᴅ ( 1/3ᴜ + 1/3ᴠ + 1/3ᴡ )
ᴅ ᴄᴀɴᴄᴇʟʟᴇᴅ ᴏᴜᴛ
= 1/ ( 1/3ᴜ + 1/3ᴠ + 1/3ᴡ )
ʟᴄᴍ ᴏғ 3ᴜ,3ᴠ ᴀɴᴅ 3ᴡ ɪs 3ᴜᴠᴡ
= 1/ ( ᴠᴡ + ᴜᴡ + ᴜᴠ ) / 3ᴜᴠᴡ
= ( 3ᴜᴠᴡ )/( ᴠᴡ + ᴜᴡ + ᴜᴠ )
ʜᴇɴᴄᴇ ᴀᴠᴇʀᴀɢᴇ sᴘᴇᴇᴅ ɪs ( 3ᴜᴠᴡ )/( ᴠᴡ + ᴜᴡ + ᴜᴠ )
ʜᴏᴘᴇ ɪᴛ ʜᴇʟᴘs
ʟᴇᴛ ᴛᴏᴛᴀʟ ᴅɪsᴛᴀɴᴄᴇ ʙᴇ ᴅ
sᴘᴇᴇᴅ = ᴅɪsᴛᴀɴᴄᴇ / ᴛɪᴍᴇ
ᴜ = 1ᴅ/3 / ᴛ1
ᴛ1 = 1ᴅ/3ᴜ
ᴠ = 1ᴅ/3 / ᴛ2
ᴛ2 = 1ᴅ/3ᴠ
ᴡ = 1ᴅ/3 / ᴛ3
ᴛ3 = 1ᴅ/3ᴡ
ᴀᴠᴇʀᴀɢᴇ sᴘᴇᴇᴅ = ᴛᴏᴛᴀʟ ᴅɪsᴛᴀɴᴄᴇ / ᴛᴏᴛᴀʟ ᴛɪᴍᴇ
= ᴅ / ( 1ᴅ/3ᴜ + 1ᴅ/3ᴠ + 1ᴅ/3ᴡ )
= ᴅ / ᴅ ( 1/3ᴜ + 1/3ᴠ + 1/3ᴡ )
ᴅ ᴄᴀɴᴄᴇʟʟᴇᴅ ᴏᴜᴛ
= 1/ ( 1/3ᴜ + 1/3ᴠ + 1/3ᴡ )
ʟᴄᴍ ᴏғ 3ᴜ,3ᴠ ᴀɴᴅ 3ᴡ ɪs 3ᴜᴠᴡ
= 1/ ( ᴠᴡ + ᴜᴡ + ᴜᴠ ) / 3ᴜᴠᴡ
= ( 3ᴜᴠᴡ )/( ᴠᴡ + ᴜᴡ + ᴜᴠ )
ʜᴇɴᴄᴇ ᴀᴠᴇʀᴀɢᴇ sᴘᴇᴇᴅ ɪs ( 3ᴜᴠᴡ )/( ᴠᴡ + ᴜᴡ + ᴜᴠ )
ʜᴏᴘᴇ ɪᴛ ʜᴇʟᴘs
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