# An object travels North at 8 ms^-1 for 9 s and then travels South at 5 ms^-1 for 3 s. What are the object's average speed and velocity?

Jul 10, 2017

Average speed = $\left(\text{total distance traveled")/("total time taken}\right) = \frac{93}{12} = 7.75$ $m {s}^{-} 1$

Average velocity = $\left(\text{total displacement")/("total time taken}\right) = \frac{63}{12} = 5.25$ $m {s}^{-} 1$ $N$

#### Explanation:

Distance traveled North:

${s}_{N} = u t = 8 \times 9 = 72$ $m$

Distance traveled South:

${s}_{S} = u t = 5 \times 3 = 15$ $m$

Total distance traveled:

$s = {s}_{N} + {s}_{S} = 78 + 15 = 93$ $m$

Total time:

$t = 9 + 3 = 12$ $s$

Average speed = $\left(\text{total distance traveled")/("total time taken}\right) = \frac{93}{12} = 7.75$ $m {s}^{-} 1$

If we take North as the positive direction, total displacement:

$s = {s}_{N} - {s}_{S} = 78 - 15 = 63$ $m$ $N$

This is the distance of the object from its starting point, and includes a direction.

Average velocity = $\left(\text{total displacement")/("total time taken}\right) = \frac{63}{12} = 5.25$ $m {s}^{-} 1$ $N$