The reason for the difference in order when calculating the change in momentum and the change in velocity is due to the definition and nature of these quantities.
Change in momentum is calculated by subtracting the momentum after an event or interaction from the momentum before. This order is used because momentum is a vector quantity that accounts for both magnitude and direction. By subtracting the momentum after from the momentum before, we can determine the net change in momentum and take into account any changes in direction.
On the other hand, change in velocity is calculated by subtracting the initial velocity from the final velocity. Velocity is also a vector quantity that includes both magnitude and direction. However, unlike momentum, velocity does not have a separate physical quantity that represents the "direction" of velocity. Instead, it is commonly expressed as a signed scalar value (with positive and negative signs denoting direction). Therefore, we subtract the initial velocity from the final velocity to determine the change in magnitude and direction of the velocity vector.
In summary, the order of subtraction when calculating change in momentum and change in velocity is based on the nature of the quantities themselves and how they are defined. Momentum accounts for both magnitude and direction, so we subtract the final momentum from the initial momentum. Velocity, on the other hand, is commonly expressed as a signed scalar value and does not have a separate direction quantity, so we subtract the initial velocity from the final velocity to calculate the change.