Question

If you divide the total distance travelled on a car trip (as determined by the odometer) by the time for the trip, are you calculating the average speed or the magnitude of the average velocity? Under what circumstances are these two quantities the same?

Short answer

If you divide the total distance traveled on a car trip by the time for the trip, you are calculating the average speed. If the car travel in a straight-line, speed will be equal to velocity.

Step-by-step solution

What are average velocity and speed?

Average Speed is defined as the ratio of total distance covered by the body to the time required to travel that distance.

$\mathbf{\text{Average\hspace{0.17em}speed\hspace{0.17em}=\hspace{0.17em}}}\frac{\mathbf{\text{Total\hspace{0.17em}distance}}}{\mathbf{\text{Total\hspace{0.17em}Time}}}$

m/s is also the measurement of average speed.

Average velocity is defined as the ratio of a body's total displacement to the time it takes to go a given distance.

$\mathbf{\text{Average\hspace{0.17em}velocity\hspace{0.17em}=\hspace{0.17em}}}\frac{\mathbf{\text{Total\hspace{0.17em}displacement}}}{\mathbf{\text{Total\hspace{0.17em}Time}}}$

The average velocity unit is also m/s.

Odometer measurement

An odometer is a device that shows the total distance covered by the vehicle. Hence if we divide that value by the time, we get the average speed.

Only in one case the average speed will be equal to the average velocity; if the vehicle is moving in a straight path.

As the vehicle moves in a straight line, the distance and the displacement will be equal. So the velocity will be the same as the speed.

Here in the figure is an example of the above case.

Figure: A car traveling on the straight path