Calculating Force - Intuition vs. Solution

[ohms law]

I'm having a little trouble conceptualizing calculations of force. The problem statement was:
An object in space with a mass of 68 kg is propelled forward at a constant force ($\vec{F}$) for 3.0 seconds. After 3.0 s, the object has moved 2.25 m. find $\vec{F}$.

I can regurgitate the proper answer (34 N) by finding $a_{x}=2 \Delta x/t^{2} = 0.50 m/s^{2}$ and $\vec{F}=ma_{x} = (68kg)(0.50 m/s^{2}) = 34 N$.

the problem is that my intuition tells me that it should be:
t = 3.0s
m = 68 kg
Δx = 2.25 m
So since $N = kg \cdot m / s^{2}$, $N = 68 kg \cdot 2.25 m / 3.0 s^{2} = 17 N$, which is obviously wrong. But, does that actually mean something else? Is that some sort of instantaneous value or something, or is it completely meaningless?

 

[Infinitum]

What you have done is basically dimensional analysis. When you do this you need to keep in mind that the expression may contain a dimensionless constant, say 'k', which you need to include. Two quantities dimensionally equal aren't necessarily the same.

So, in your case it would be,

$$F \alpha [M][L][T]^{-2}$$

Therefore,

$$F = k * MLT^{-2}$$

Where the value of k is...?

...And, I feel good to be able to post again.