instantaneous+vs+average+velocity

go back to kinematics Before going to the explanations of instantaneous and average velocities, let us begin by assuming things. Let us all assume that the given data, tables, and graphs below are true, Ceteris Paribus. A car is being driven into a single direction all throughout. The car travels at constant acceleration. i.e. Acceleration pays no part in this demonstration. The displacement and its respective time intervals are recorded and expressed as is in the following table.
 * < t (seconds) ||< d (meters) ||
 * < 1.00 ||< 1.00 ||
 * < 1.10 ||< 1.21 ||
 * < 1.50 ||< 2.25 ||
 * < 2.00 ||< 4.00 ||
 * < 3.00 ||< 9.00 ||
 * < 5.00 ||< 25.00 ||
 * < 9.00 ||< 81.00 ||

To the right is a graph of the data in the chart:
=Average velocity= Average velocity is defined as simply, change in displacement over change in time. In the given example, we would be able to express average velocity from the given data as the following: Nevertheless, a better value could be achieved through the usage of the best-fitted line because the graph is an exponential one. The slope of the best-fitted line would give you an idea of the average velocity somewhat better. In this case, it would be 9.825, which is not too far from the 10.0 we derived. =Instantaneous velocity= Instantaneous velocity, on the other hand, is a little more complicated. Instantaneous velocity is the velocity at a single time interval. Also, a more accurate instantaneous velocity can be achieved as the time interval becomes closer to 0. So, let us choose two points from the graph. (4.9, 24.01) and (5, 25). Now, we must calculate for the slope, average velocity, of these two points like the following:  So, this will be the approximation of instantaneous velocity for the time intervals 4.9 secs to 5 secs. To get the closest value of the instantaneous velocity, you would have to get the tangent line of a given point and get its slope.