# An object travels North at  7 m/s for 6 s and then travels South at  3 m/s for  8 s. What are the object's average speed and velocity?

Apr 30, 2016

Speed=$\frac{33}{7} \frac{m}{s}$and velocity $= \frac{9}{7} \frac{m}{s}$

#### Explanation:

Distance traveled due North in 6s @ $7 \frac{m}{s}$ is =$7 \times 6 = 42 m$
Distance traveled due South in 8s @ $3 \frac{m}{s}$ is =$3 \times 8 = 24 m$
Total Distance traveled $= 42 m + 24 m = 66 m$
Total time taken = $6 + 8 = 14 s$
So average speed $= \frac{T o t a l D i s \tan c e}{t i m e} = \frac{66}{14} \frac{m}{s} = \frac{33}{7} \frac{m}{s}$

Now net displacement due North=$42 - 24 = 18 m$ (North,South being oppositely directed)

Hence Average velocity due North$= \frac{D i s p l a c e m e n t}{T i m e} = \frac{18}{14} \frac{m}{s} = \frac{9}{7} \frac{m}{s}$