The product of the force and the time for which it acts is called the impulse of the force and is denoted by the symbol J.
J = Ft
Therefore impulse = change in momentum
J = mv – mu
This relationship shows that impulse, too, is a vector quantity. Hence, if a force exerts an impulse on an object in a direction opposite to that of motion, the impulse is negative. It follows that the change in momentum is negative, i.e. the final momentum is less than the initial momentum.
As with all problems involving vector quantities, it is important when dealing with impulse and momentum to define the chosen positive direction.
Although readers will often find that I is used as the symbol for impulse, we prefer to use J. Our reason is that at a further stage in the study of mechanics (beyond the scope of this book) a completely different quantity is represented by I.