Newton's second law of motion in the context of "Impulse (physics)"

In classical mechanics, impulse (symbolized by J or Imp) is the change in momentum of an object. If the initial momentum of an object is p₁, and a subsequent momentum is p₂, the object has received an impulse J:$${\displaystyle \mathbf {J} =\mathbf {p} _{2}-\mathbf {p} _{1}.}$$

Momentum is a vector quantity, so impulse is also a vector quantity:$${\displaystyle \sum \mathbf {F} \times \Delta t=\Delta \mathbf {p} .}$$Newton's second law of motion states that the rate of change of momentum of an object is equal to the resultant force F acting on the object:$${\displaystyle \mathbf {F} ={\frac {\mathbf {p} _{2}-\mathbf {p} _{1}}{\Delta t}},}$$so the impulse J delivered by a steady force F acting for time Δt is:$${\displaystyle \mathbf {J} =\mathbf {F} \Delta t.}$$