Question

An object travels North at `1 m/s` for `8 s` and then travels South at `6 m/s` for `4 s`. What are the object's average speed and velocity?

Answer 1

Average speed: `2 2/3 m/scolor(white)("XXX")`Average velocity: `1 1/3 m/s ["South"]`

Explanation:

The object travels:
`color(white)("XXX")`North: `1 m/s xx 8 s =8 m`
`color(white)("XXX")`South: `6 m/s xx 4 s =24 m`

For a total distance of `32 m`
and
`color(white)("XXX")`(noting that `24 m" South" = -24 m" North"`)
a resulting displacement of `8 m (N) - 24 m (N)=-16 m (N)`

Total travel time: `8 s + 4 s = 12 s`

Average speed `= ("total distance")/("total time")= (32 m)/(12 s)=2.66bar6 m/s`

Average velocity`=("resulting displacement")/("total time")=(-16 m "(N)")/(12 s)=-1.33bar3 m/s "(N)"`

`color(white)("XXX")`or`color(white)("XXXXXXXXXXXXXXXXXXXXXX")+1.33bar3 m/s "(S)"`

Notice that displacement and velocity should always contain a component indicating direction.