According to Newton's Second Law, does an instantaneous force cause an object to reach the velocity of its acceleration?

Alex, what's "instantaneous"? How long is it? ...a hundredth of a second?.....a thousandth of a second? You don't need physics to know from experience that the longer you push on something the faster it will go. So the simple answer to your question, ignoring physics, is the velocity the object attains will depend upon its mass and how long you apply the force.

Now lets go back to your original question and examine it from a mathematical perspective. If F = ma, and the force is 100 newton's and the mass is 10 kg, then the acceleration will be a = F/m or 100/10 (100 kg. m^2/s^2/10 kg). This equals an acceleration of 10 m/sec^2. That acceleration will occur for as long as the force is applied. In practical terms what that means is that the velocity will increase 10 meters per second, each second the force is applied. So at the end of the first second, the velocity will be 10 m/s and at the end of the 2nd. second the velocity will be 20 m/s. Now suppose you apply the force for 0.1 seconds. That's certainly not instantaneous, but it's a really brief time. How fast will the 10 kg object be going? We've already calculated that the acceleration is 10 meters/second. So we can calculate the final velocity by simply realizing that the velocity will

be equal to the acceleration times the amount of time it acts, (v = at). So for 0.1 seconds the velocity will be (10 m/sec^2)(0.1 sec) = 1 meter per second. If your instantaneous push was 0.01 seconds, the velocity would be 0.1 meter/second. Do you see? I hope so. Alex, don't let the math scare you. Often the concepts being taught are really common sense. It's just that physics isn't just concerned with ideas, but with mathematically analyzing the results of the idea. Of course, some things, like this acceleration problem are not completely obvious. For example, it's hard for people to believe that once an object starts moving it will keep moving forever. That's because friction exists down here, but in space there's nothing to stop something from moving forever. I was (and am) amused by films like Star Trek in which if their warp drive fails, they stop. That's absurd of course, but most people who go to movies aren't physicists.

Acceleration and velocity are NOT the same.

It accelerates which means that it gains velocity.

It gains a very small amount in a very small time.

It gains more in a longer time.

If you got out onto your bike you would already be well aware of this.

Stand on the pedals for a second and you would reach maybe 1 mph

Yet if you keep pressing on those pedals for thirty seconds or more ( assuming you are fit enough to do this ) then your speed will be many times higher.

You would need to put a time on the 'instant'.

Acceleration = (f/m), = (100/10) = 10m/sec^2.

But to have it reach 10m/sec. velocity, the 'instant' would need to be (v/a) = (10m.sec/10m/sec^2) = 1 second.

So its velocity depends on the time the acceleration is applied, e.g. if you apply the 100N. for 10 secs., the V would be (at) = (10 x 10) = 100m/sec.