Why is displacement used in the formula for velocity instead of distance?

[Taterpeel]

Hello everyone. I want to learn Physics, so I've been trying to teach myself. I still don't know much, and am just now getting to the formula for Velocity. The internet tutorial I am using says it is this..

Average Velocity = Displacement / Elapsed Time

And I've been plugging in the numbers, and it's not hard or anything. I was just wondering.. Why would displacement be in the numerator? Shouldn't it be distance? If I travel somewhere and then travel back to my destination 30 times in an hour, won't my velocity be different than if I do it 5 times? But I will end up with the same Displacement, so why do I use displacement here, and not distance?

 

[russ_watters]

Velocity is a vector quantity. It includes direction. So if you travel around and eventually end up where you started, your average velocity was zero.

Ie, if you travel one direction for an hour at 60 mph and travel back to where you started also at 60 mph, that's 60*1+(-60)*1=0 displacement. Average velocity is (60+(-60))/2=0 But speed is a scalar quantity, so your average speed is (60+60)/2=60.

 

[charng]

Displacement is used in the formula for velocity because it represents the change in position of an object. Distance, on the other hand, is the total length of the path traveled by the object. In the context of velocity, it is important to consider the direction of motion and the change in position, rather than just the total distance traveled.

For example, imagine you are driving a car in a circular track. If you complete one lap around the track and return to your starting point, your total distance traveled would be the circumference of the track. However, your displacement would be zero, as your starting and ending positions are the same. This means that your velocity would also be zero, even though you have traveled a significant distance.

In contrast, if you were to travel from point A to point B and then back to point A, your displacement would be the distance between those two points, regardless of how many times you traveled back and forth. This allows for a more accurate measurement of the object's motion and velocity.

Additionally, using displacement in the formula for velocity allows us to consider the direction of motion. If an object travels from point A to point B and then back to point A, but in the opposite direction, its displacement would be the same, but its velocity would be negative, indicating a change in direction.

In summary, displacement is used in the formula for velocity because it takes into account the direction of motion and the change in position, providing a more accurate measurement of an object's velocity.