Question

An object travels North at `7 m/s` for `5 s` and then travels South at `9 m/s` for `2 s`. What are the object's average speed and velocity?

Answer 1

`vecV_"net"=2.43m/s->"towards north"`

`V_"avg" ~~7.6m/s`

Explanation:

For 1st 5s the velocity of the object towards North be
`vecV_"north"=7hatjm/s`

For 1st 5s the displacement of the object towards North be
`vecd_"north"=7hatjm/sxx5s=35hatjm`

For 2nd 2s the velocity of the object towards Southbe `vecV_"south"=-9hatjm/s`

For 2nd 2s the displacement of the object towards Southbe `vecd_"south"=-9hatjm/sxx2s=-18hatjm`

Net displacement during t=(5+2)=7s is
`vecd_"net"=35hatjm-18hatjm=17hatjm->"towards north"`

Hence the Net Velocity
`vecV_"net"=vecd_"net"/t=17/7hatjm=2.43m/s->"towards north"`

Total distance covered during 7 s
`d_"total"=|vecd_"north"|+|vecd_"south"|=|35hatjm|+|-18hatjm|=53m`

Hence Average speed
`V_"avg" = d_"total"/t=53/7m/s~~7.6m/s`