# An object travels North at # 3 m/s# for #7 s# and then travels South at # 4 m/s# for # 4 s#. What are the object's average speed and velocity?

Please see the explanation below.

The overall distance traveled is

To travel this distance in time, it is

The typical pace is

The actual distance traveled is

The mean speed is

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The object's average speed is ( \frac{{\text{total distance}}}{{\text{total time}}} = \frac{{(3 , \text{m/s} \times 7 , \text{s}) + (4 , \text{m/s} \times 4 , \text{s})}}{{7 , \text{s} + 4 , \text{s}}} = \frac{{21 , \text{m} + 16 , \text{m}}}{{11 , \text{s}}} = \frac{{37 , \text{m}}}{{11 , \text{s}}} \approx 3.36 , \text{m/s}). The object's average velocity is ( \frac{{\text{total displacement}}}{{\text{total time}}} = \frac{{(0 , \text{m/s} - 3 , \text{m/s}) + (0 , \text{m/s} - 4 , \text{m/s})}}{{7 , \text{s} + 4 , \text{s}}} = \frac{{-3 , \text{m/s} - 4 , \text{m/s}}}{{11 , \text{s}}} = \frac{{-7 , \text{m}}}{{11 , \text{s}}} \approx -0.64 , \text{m/s}).

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