I was looking through an old copy of Barron's AP Physics and found this problem relating to impulse which I was initially confused about how to integrate.
Example 6.1 During a collision with a wall lasting from $t=0$ to $t=2\text{ s}$, the force acting on a $2\text{-kg}$ object is given by the equation $\mathbf{F} = (4\mathrm{\ kg\ m/s^4})t(2s-t)\hat{i}$
They work out that the integral is equal to:
$$\frac{16}{3}\hat{i}\frac{\text{kg m}}{\text{s}}$$
I am confused about the role of the units in the problem.
Looking at the answer, it seems that if I were to just ignore all the units and simply integrate $4t\cdot(2-t)$ that would give me $16/3$, and because that is a force I know it to be $\mathrm{kgm/s}$$\mathrm{kg\,m/s}$ or $\mathrm{N}$.
Why it would be OK to ignore the units in the integral though is somewhat unintuitive to me (other than that I know the end result must be a force) and I feel like it may get me into trouble with other problems.
Can someone explain how it is that the scalar values of the original unit quantities still give you the correct answer?
And also, what exactly is a kilogram metre per second ^ 4? Is there any way to easily perceive what that is?
