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**1. Homework Statement**

I am having a bit of confusion regarding this:

When you write dr/dt (rate of change of position vector with time, sorry I don't know how to use LATEX), do you mean instantaneous or average velocity?

As we are considering a very small time interval, I guess it is instantaneous. Now, can we define average velocity in the same way? (Δr/Δt which spans over a bigger time interval)

However, I also saw a few problems on calculating average velocity over a time interval in projectile motion, and they are calculating it by differentiating (ucosθt i + usinθt-0.5gt

^{2}j), which is the position vector at an instant. Now, if instantaneous velocity is dr/dt, and not average velocity, then how can one proceed like this?

Please explain me.

**2. Homework Equations**

**3. The Attempt at a Solution**