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?

Apr 8, 2017

Average speed: $2 \frac{2}{3} \frac{m}{s} \textcolor{w h i t e}{\text{XXX}}$Average velocity: $1 \frac{1}{3} \frac{m}{s} \left[\text{South}\right]$

Explanation:

The object travels:
$\textcolor{w h i t e}{\text{XXX}}$North: $1 \frac{m}{s} \times 8 s = 8 m$
$\textcolor{w h i t e}{\text{XXX}}$South: $6 \frac{m}{s} \times 4 s = 24 m$

For a total distance of $32 m$
and
$\textcolor{w h i t e}{\text{XXX}}$(noting that $24 m \text{ South" = -24 m" North}$)
a resulting displacement of $8 m \left(N\right) - 24 m \left(N\right) = - 16 m \left(N\right)$

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

Average speed $= \left(\text{total distance")/("total time}\right) = \frac{32 m}{12 s} = 2.66 \overline{6} \frac{m}{s}$

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

$\textcolor{w h i t e}{\text{XXX}}$orcolor(white)("XXXXXXXXXXXXXXXXXXXXXX")+1.33bar3 m/s "(S)"

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