# An object travels North at  4  ms^-1 for 3 s and then travels South at  6  ms^-1 for  8  s. What are the object's average speed and velocity?

Apr 28, 2016

The average speed is the total distance over the time, the average velocity is the total displacement over time. Speed = $5.45$ $m {s}^{-} 1$, velocity = $3.27$ $m {s}^{-} 1$.

#### Explanation:

Find the distances traveled in each step:

$d = v t = 4 \cdot 3 = 12$m N

$d = v t = 6 \cdot 8 = 48$m S

The total distance is the simple sum of these two distances, $60$ $m$.

The total displacement is the difference between them, $36$ $m$ S

The total time is $8 + 3 = 11$ $s$

To find the average speed:

$s p e e d = \left(\text{distance")/("time}\right) = \frac{60}{11} \approx 5.45$ $m {s}^{-} 1$

To find the average velocity:

$v e l o c i t y = \left(\text{distance")/("time}\right) = \frac{36}{11} \approx 3.27$ $m {s}^{-} 1$