# An object travels North at 6 m/s for 8 s and then travels South at 2 m/s for 5 s. What are the object's average speed and velocity?

Mar 23, 2017

${s}_{a v} = 4.5 \text{m/s}$
$\vec{{v}_{a v}} = 2.9 \text{m/s North}$
The object travels $6 \text{m/s"*8"s"=48"m}$ north and $2 \text{m/s"*5"s"=10"m}$ south in a total time of $8 \text{s"+5"s"=13"s}$
Average speed refers to total distance over time, regardless of direction. Since the object covers a total distance of $48 \text{m"+10"m"=58"m}$ in $13 \text{s}$, its average speed is d/(Deltat)=(58"m")/(13"s")~~4.5"m/s"
Average velocity is a bit more complicated because direction matters; average velocity refers to displacement over time. Let's assign positive to be north for this problem. Since the object has a total displacement of ("+"48"m")+("-"10"m")=48"m"-10"m"="+"38"m" in the same $13 \text{s}$, its average velocity is (Deltavecx)/(Deltat)=("+"38"m")/(13"s")~~"+"2.9"m/s", so $2.9 \text{m/s North}$