Question

If you divide the total distance traveled 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?

a) Average speed; they are always the same.

b) Magnitude of average velocity; they are always the same.

c) Average speed; they are the same if the car moves in a straight line.

d) Magnitude of average velocity; they are the same if the car moves in a straight line.

Answer 1

Average speed is found by dividing the total distance traveled by the time for the trip, while the magnitude of average velocity is found by dividing the magnitude of the total displacement by the elapsed time. These two quantities are the same when the car is traveling at a constant speed and does not change its direction.

Step-by-step explanation:

Average speed is not necessarily the same as the magnitude of the average velocity. Average speed is found by dividing the total distance traveled by the time for the trip, while the magnitude of average velocity is found by dividing the magnitude of the total displacement by the elapsed time. These two quantities are the same when the car is traveling at a constant speed and does not change its direction.

For example, if a car travels in a straight line at a constant speed from point A to point B and then returns from point B to point A at the same constant speed, the total distance traveled is equal to the magnitude of the total displacement. Therefore, the average speed and the magnitude of the average velocity would be the same in this case.