The equations for change in momentum and change in velocity are derived from different principles and concepts in physics, which is why their expressions may appear different.
The change in momentum of an object is given by the equation Δp = p_f - p_i, where Δp represents the change in momentum, p_f is the final momentum, and p_i is the initial momentum. This equation is based on the principle of conservation of momentum, which states that the total momentum of an isolated system remains constant unless acted upon by external forces. By subtracting the initial momentum from the final momentum, you obtain the change in momentum experienced by the object.
On the other hand, the change in velocity of an object is given by the equation Δv = v_f - v_i, where Δv represents the change in velocity, v_f is the final velocity, and v_i is the initial velocity. This equation arises from the concept of velocity, which is defined as the rate of change of displacement. By subtracting the initial velocity from the final velocity, you obtain the change in velocity experienced by the object.
The choice of order in these equations is based on the convention and mathematical simplicity. In both cases, subtracting the initial value from the final value gives you the change experienced by the object. However, the specific equations for momentum and velocity arise from different physical principles and mathematical relationships, leading to the difference in their expressions.