Impulse is the product of force and time

Impulse.?

A moving object has momentum. It can give an impulse to another object and in the process receive an impulse. Both will have their momenta changed, but the law of conservation of momentum holds good.
It won’t be proper to say that an object has impulse. You can say that an object gives or receives an impulse which is the same as saying “ an object changes the momentum of another object and gets its own momentum changed”.

 

F = ma, right? Also, F = m(dv/dt), right? Therefore, F = d(mv)/dt = dp/dt, right?

Now, multiply by dt on both sides to get Fdt = dp. But Fdt is dI. So, dI = dp. A differential increase in impulse is equal to a differential increase in momentum.

Or, we can integrate both sides of the equation Fdt = dp. The integral of Fdt is the total Impulse, I , and the integral of dp is total momentum, p. Therefore I = p. So, if an object has momentum p then it has recieved a total impulse of I at some point.

Keep in mind that we are assuming zero initial conditions, so that the impulse at the time before the force F was applied is ZERO, and therefore the initial momentum is zero.

Simple as that.

A moving object with a certain amount of momentum received an impulse at one point in order to gain the momentum it has. But if its momentum is now constant then there is no force applied (dp/dt = F = 0) and therefore there is no increase in total impulse.

But I suppose you can say that an object moving at a constant velocity of 5 m/s has an impulse even if the force is zero at present, because at a certain time in the past the object's force curve was non-zero, and therefore it had an impulse. Again, impulse is the integral of the force-time curve for an object, and even if the force is currently zero doesn't mean it was zero at some time in the past. And a F vs. t graph that is zero at time t = 5 seconds doesn't mean it is zero at time t = 2 seconds. The object still has an impulse even at time t = 5 seconds because there was area underneath the curve in the past.

 

I think the question of using the term ‘impulse’ comes into picture when a force comes in to play. Otherwise you will have to say that all moving bodies have impulse and the terms ‘impulse’ and ‘momentum’ will have to be used without any distinction. [You never think of the term ‘impulse’ in the case of a body in uniform motion]. It is the ‘force’ which is to be given the importance when one uses the term ‘impulse’. This is only a question of proper usage of terms even when we agree that impulse is equal to the change in momentum.