# An object travels North at  6 m/s for 6 s and then travels South at  3 m/s for  7 s. What are the object's average speed and velocity?

May 1, 2018

$A v g . S p e e d = \frac{57}{7} m {s}^{-} 1$
$A v g . V e l o c i t y = \frac{15}{13} m {s}^{-} 1$ (northwards)

#### Explanation:

$A v g S p e e d = \frac{T o t a l D i s t .}{T o t a l t i m e}$
$= \frac{6 \times 6 + 3 \times 7}{6 + 7} = \frac{57}{13} \frac{m}{s}$
(Distance = Speed x Time)
Total Displacement is 36 - 21. The object went 36 m north and then 21 m south. Thus it is displaced by 15 m from its origin. $A v g . V e l o c i t y = \frac{T o t a l D i s p l a c e m e n t}{T o t a l t i m e}$
$= \frac{15}{6 + 7} = \frac{15}{13} \frac{m}{s}$

You may wish to specify that the displacement is in the north direction.