An object travels North at #6 m/s# for #9 s# and then travels South at #6 m/s# for #7 s#. What are the object's average speed and velocity?

Question

An object travels North at #6  m/s# for #9 s# and then travels South at #6  m/s# for #7 s#.  What are the object's average speed and velocity?

Adrian Ayala · Accepted Answer

The average speed is 6m/s; the average velocity is 0.75 m/s North.

First, we must determine the displacement of the object during each time interval. During the first 9s #d=vxxt = 6m/sxx9s = 54m# North During the next 7s #d=vxxt = 6m/sxx7s = 42m# South For the average speed , we consider only the total distance travelled and the total time taken #v_"ave" = d-:t = 96 m-:16 s = 6 m/s# For the average velocity , we consider the net displacement and the time taken. The net displacement has been only 12 m North. #vecv_"ave"=vecd -:t = 12m N -: 16s = 0.75 m/s # North

Elena Albarran · Answer

undefined Average Speed: $ \frac{{\text{{Total Distance}}}}{{\text{{Total Time}}}} $

Average Velocity: $ \frac{{\text{{Displacement}}}}{{\text{{Total Time}}}} $

1. **Calculate total distance traveled:**
   $$ \text{{Total Distance}} = (\text{{Distance North}}) + (\text{{Distance South}}) $$

2. **Calculate displacement:**
   $$ \text{{Displacement}} = (\text{{Distance North}}) - (\text{{Distance South}}) $$

3. **Calculate average speed:**
   $$ \text{{Average Speed}} = \frac{{\text{{Total Distance}}}}{{\text{{Total Time}}}} $$

4. **Calculate average velocity:**
   $$ \text{{Average Velocity}} = \frac{{\text{{Displacement}}}}{{\text{{Total Time}}}} $$

Given the values for time, velocity, and direction, substitute into the formulas to find the average speed and velocity.