An object travels North at 6 m/s for 5 s and then travels South at 7 m/s for  5 s. What are the object's average speed and velocity?

Jan 14, 2018

Average speed $= 6.5 \frac{m}{s}$
Average velocity$= - 0.5 \frac{m}{s}$

Explanation:

Average $\text{velocity" = "displacement"/"time elapsed}$
$\overline{v} = \frac{\Delta x}{\Delta t}$
Average $\text{speed" = "distance traveled"/"time elapsed}$
$\overline{s} = \frac{d}{\Delta t}$

Going north at 6m/s for 5s is 30m, and going south at 7m/s for 5s is 35m, hence the object in 10s has effectively gone south for 5m as a displacement despite it has actually traveled a total distance of 65m.

Bear in mind that for displacement going north is positive, south negative:

$\Delta x = 6 \frac{m}{s} \cdot 5 s - 7 \frac{m}{s} \cdot 5 s = 30 m - 35 m = - 5 m$

$d = 30 m + 35 m = 65 m$

$\Delta t = 5 s + 5 s = 10 s$

$\overline{v} = \frac{\Delta x}{\Delta t} = - \frac{5 m}{10 s} = - 0.5 \frac{m}{s}$
$\overline{s} = \frac{d}{\Delta t} = \frac{65 m}{10 s} = 6.5 \frac{m}{s}$