Question

An object travels North at `1 m/s` for `8 s` and then travels South at `7 m/s` for `5 s`. What are the object's average speed and velocity?

Answer 1

Average Speed = `3.31ms^-1`
Average Velocity = `-2.08ms^-1` North (`2.08ms^-1` South)

Explanation:

Speed does not rely on the direction of movement so:
`"Average speed" = "Displacement (total distance travelled)"/"Time"`

Displacement (`s`) = Displacement 1 (`s_1`) + Displacement 2 (`s_2`)
`s="speed"xxDeltat`
`s_1=1ms^-1xx8s=8m`
`s_2=7ms^-1xx5s=35m`

`s_("total")=8m+35m=43m`
Time (total) = `8s+5s=13s`

`"Average Speed"=s/t=(43m)/(13s)=3.31ms^-1`

---

Velocity is reliant on the direction of travel so:

`"Velocity ("v")"=("Final distance from start ("d_"total"")")/("Time ("t")"`

Here we use velocity (`v`) with a direction so that movement North is positive (and movement South is negative)
`Deltad=vxxDeltat`
`d_1=1ms^-1xx8s=8m`
`d_2=-7ms^-1xx5s=-35m`

`d_"total"=d_1+d_2=8m+(-35m)=-27m`

`v=(d_"total")/(t_total) = (-27m)/(13s)=-2.08ms^-1 " North"`
You could also say the velocity is `2.08ms^-1 South`. Since both are equivalent, both are correct, as long as you give the correct direction to go with the answer.