# An object travels North at 9 m/s for 5 s and then travels South at 6 m/s for  3 s. What are the object's average speed and velocity?

average speed \bar v=7.875\ \text{m/s

velocity  v=6.058\ \text{m/s

#### Explanation:

Average speed

$\setminus \overline{v} = \setminus \frac{\setminus \textrm{\to t a l \mathrm{di} s \tan c e t r a v e \le d}}{\setminus \textrm{\to t a l t i m e}}$

$= \setminus \frac{{v}_{1} {t}_{1} + {v}_{2} {t}_{2}}{{t}_{1} + {t}_{2}}$

$= \setminus \frac{9 \setminus \times 5 + 6 \setminus \times 3}{5 + 3}$

$= \setminus \frac{63}{8}$

$= 7.875$

hence average speed \bar v=7.875\ \text{m/s

Velocity

$v = \setminus \frac{\setminus \textrm{\mathrm{di} s p l a c e m e n t}}{\setminus \textrm{\to t a l t i m e}}$

$= \setminus \frac{\setminus \sqrt{{\left({v}_{1} {t}_{1}\right)}^{2} + {\left({v}_{2} {t}_{2}\right)}^{2}}}{{t}_{1} + {t}_{2}}$

$= \setminus \frac{\setminus \sqrt{{\left(9 \setminus \times 5\right)}^{2} + {\left(6 \setminus \times 3\right)}^{2}}}{5 + 3}$

$= \setminus \frac{9 \setminus \sqrt{29}}{8}$

$= 6.058$

hence the velocity  v=6.058\ \text{m/s