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Its about Newton's second law of motion,

$$F=ma.$$

It says the acceleration of an object is directly proportional to the net force and is inversely proportional to the object's mass. Yes I can imagine that. But there's still something I don't really understand but I don't know what it is..

I know its a stupid question but i am just confusing...
I mean, in math: $$\mathrm{acceleration=(final\ velocity-initial\ velocity)/time\ elapsed}$$ But, in physics, $a=F/m $

Does that mean $F/m = \mathrm{(final\ velocity-initial\ velocity)/time\ elapsed}$ ?

and how did Newton find out forces has something to do with acceleration and mass?

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    $\begingroup$ Galileo's law of falling bodies established that uniform forces result in uniform acceleration. But this uniform force is just the weight an object experiences due to gravity, which was known since ancient times from practical experience with scales to be proportional to an object's "amount of substance". Further experiments with different forces, say springs, reveal that the ratio of force to acceleration is a constant property of any particular object. $\endgroup$
    – David H
    Apr 15, 2013 at 16:50

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Like Rafael says, the formula for acceleration is right. $$\frac{v_2-v_1}t=\frac{F}{m}$$

Regarding the heading (which is quite different from the actual question)

How did Newton find out force has something to do with acceleration?

He was quite smart to correct Aristotle's original formula for force $F=mv$ (now taken as the momentum $p$) which appears right regarding moving objects that when you apply a force, you get a velocity on the object.

But, when you apply a force on the object, you change its velocity from zero ($v_1$) to some value $v_2$. The symmetry is also possible that when you apply a force on the moving object ($v_1$), it comes to rest ($v_2=0$). By this way, Newton figured out that when you apply a force, you change the velocity of the object (which is acceleration).

The reasoning that force depends on the inertial mass of the object is already figured out by Aristotle. Newton just modified it. And, Aristotle was right about the dependency on inertial mass. Because, the more an object has mass - you require a larger force to push / pull or stop it from motion. This is an inability of massive objects called inertia...

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