Average Velocity & Instantaneous Velocity
Average Velocity
In physics, the phrase average velocity is used in two different ways:
In physics, the phrase average velocity is used in two different ways:
- Average velocity is used to describe the motion of an object that we have good reason to expect travels at a constant velocity. Our model of motion at a constant velocity states that the object travels equal distances during equal time intervals. However, measurement data will always show some variations due to several sources of experimental uncertainty. So, the best we can do is to determine the average distance traveled during each time interval of one unit and report that value (along with the uncertainty interval) as the constant average velocity of the object.
- Average velocity is also used when the object definitely does not travel at a constant velocity;
for example, when there are abrupt changes of speed or direction, or when the speed or direction changes gradually over time. In these situations, the average velocity is that constant velocity which accomplishes the same total displacement during the same total time interval as did the changing velocity. The following examples refer to this use of average velocity.
The Mean Value Theorem of Calculus
For the special case of the quadratic function, the tangent to the arc is parallel to the secant at the midpoint of the interval over which the secant was drawn. Just sayin', again.
This means that, for the special case of motion with constant acceleration, the average velocity over a time interval is equal to the instantaneous velocity at the midpoint of the time interval.
This means that, for the special case of motion with constant acceleration, the average velocity over a time interval is equal to the instantaneous velocity at the midpoint of the time interval.
Instantaneous Velocity