Question

Is initial velocity and final velocity instantaneous?

Answer 1

Since, we know as the body changes its position with time the concept of velocity is introduced. The velocity is a vector quantity which is known as the rate of change of position. The faster the body changes its position with time the greater the velocity of the body. The change of position with time is mentioned as $\vec x(t)$ and for velocity as a function of time is $\vec v(t)$ .

Complete step by step answer:
Yes, the initial velocity and final velocity are instantaneous. We can define velocity as the differentiation of position with respect to time i.e. $\vec v(t) = \dfrac{{d\vec x(t)}}{{dt}}$ . As the displacement of the body is a function of time $\vec x(t)$ .
We don't usually place the arrow marks at the top of these quantities for the purpose of simplicity, but we always understand them as vectors.
Suppose,
Initial velocity is velocity of the body at time $t = \mathop t\nolimits_i$
Final velocity is velocity of the body at time $t = \mathop t\nolimits_f$
So, initial velocity = $\vec v(\mathop t\nolimits_i )$
And final velocity = $\vec v(\mathop t\nolimits_f )$
Now, it can easily be depicted as at $t = \mathop t\nolimits_i + \delta t$
Velocity = $\vec v(\mathop t\nolimits_i + \delta t)$
There is a very small change in time from the initial time.
So, we can see that velocity is different from initial velocity depending upon the time. The same condition holds true for the final velocity too.

Note: We know that the displacement is the quantity that can be understood for the change in the position. If the position changes with time it is termed as velocity. Since, direction is always a necessary condition for these quantities so they are called vector quantities. Velocity as we have seen changes for a very small change in time.