# An object travels North at  2 m/s for 6 s and then travels South at  7 m/s for  9 s. What are the object's average speed and velocity?

Aug 14, 2017

The average speed is $= 5 m {s}^{-} 1$
The average velocity is $= 3.4 m {s}^{-} 1$

#### Explanation:

The total distance travelled is $d = \left(2 \cdot 6\right) + \left(7 \cdot 9\right) = 12 + 63 = 75 m$

The total time is $t = 6 + 9 = 15 s$

The average speed is

$\overline{v} = \frac{d}{t} = \frac{75}{15} = 5 m {s}^{-} 1$

The displacement is

$\Delta x = \left(2 \cdot 6\right) - \left(7 \cdot 9\right) = 12 - 63 = - 51 m$

The average velocity is

$= \frac{\Delta x}{t} = | - 51 \frac{|}{15} = 3.4 m {s}^{-} 1$