# An object travels North at  8 m/s for 9 s and then travels South at  5 m/s for  2 s. What are the object's average speed and velocity?

May 11, 2016

${v}_{a} = 5.64 \text{ } \frac{m}{s}$

${u}_{a} = 7.45 \text{ } \frac{m}{s}$

#### Explanation:

$\vec{A} B = 8 \cdot 9 = 72 \text{ } m$
$\vec{C} D = 5 \cdot 2 = 10 \text{ } m$

$\text{distance="AB+CD=72+10=82 " } m$
$\text{displacement="vec AB-vec CD=72-10=62 " } m$

$\text{average velocity} = \frac{\mathrm{di} s p l a c e m e n t}{t i m e}$

${v}_{a} = \frac{62}{9 + 2}$

${v}_{a} = \frac{62}{11}$

${v}_{a} = 5.64 \text{ } \frac{m}{s}$

$\text{average speed=} \frac{\mathrm{di} s \tan c e}{t i m e}$

${u}_{a} = \frac{82}{11}$

${u}_{a} = 7.45 \text{ } \frac{m}{s}$