Question

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

Answer 1

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