# An object travels North at 4 m/s for 9 s and then travels South at 6 m/s for  2 s. What are the object's average speed and velocity?

Average Speed $= \frac{48}{11} = 4. \overline{36}$m/sec
Average Velocity $= \frac{24}{11} = 2. \overline{18} \text{ }$m/sec directed North

#### Explanation:

The given data

Directed North ${v}_{1} = 4 \text{ }$m/sec for time ${t}_{1} = 9 \text{ }$sec
Directed South ${v}_{2} = 6 \text{ }$m/sec for time ${t}_{2} = 2 \text{ }$sec

distance ${d}_{1} = {v}_{1} \cdot {t}_{1} = 4 \cdot 9 = 36 \text{ }$m
distance ${d}_{2} = {v}_{2} \cdot {t}_{2} = 6 \cdot 2 = 12 \text{ }$m

Average speed $= \frac{{d}_{1} + {d}_{2}}{{t}_{1} + {t}_{2}} = \frac{36 + 12}{9 + 2} = \frac{48}{11} = 4. \overline{36} \text{ }$m/sec

Average Velocity $= \frac{+ 36 + \left(- 12\right)}{9 + 2} = \frac{24}{11} = 2. \overline{18} \text{ }$m/sec

God bless....I hope the explanation is useful.