# An object travels North at  5 m/s for 1 s and then travels South at  3 m/s for  3 s. What are the object's average speed and velocity?

Feb 27, 2017

$S a v = 3.5 \frac{m}{s}$; $V a v = 1 \frac{m}{s}$ South

#### Explanation:

Travel distance north is $5 \frac{m}{s} \times 1 s = 5 m$ (shorter)

Travel distance south is $3 \frac{m}{s} \times 3 s = 9 m$ (longer)

Average speed is the total distance travelled divided by total time.

$S a v = \frac{5 m + 9 m}{1 s + 3 s} = \frac{14 m}{4 s} = 3.5 \frac{m}{s}$

Average velocity is the resultant change in velocity divided by the total time where the final velocity is South;

$V a v = - V n + V s$

Note that $V n$ is negative because its direction is opposite to the final velocity.

$V a v = \frac{- 5 m n + 9 m s}{1 s + 3 s} = \frac{4 m}{4 s} = 1 \frac{m}{s} S o u t h$

This scenario may occur in real life when a ping pong ball is returned from a serve.