Why my expression for acceleration doesn't work? So i have an object that moves in a straight line with initial velocity $v_0$ and starting position $x_0$. I can give it constant acceleration $a$ over a fixed time interval $t$. Now what i need is that when the time interval ends this object should stop exactly at a point $x_1$ with it's velocity being equal to $0$. I need to find acceleration $a$ that i can give it in order for that to happen. 
The way i see it we've got a system of equations: 
$$ 0 = v_0 + a t $$
$$ x_1 = x_0 + v_0 t + \frac {a t^2} {2} $$ 
I have only one unknown, which is $a$. 
Let's get $a$ from the first equation: 
$$ a = \frac { - v_0 } { t } $$ 
And put it into the second one: 
$$ x_1 = x_0 + v_0 t + \frac { - v_0 t } {2} $$ 
Now let's express initial velocity ($v_0$) from that equation: 
$$ x_1 - x_0 = v_0 t + \frac { - v_0 t } {2} $$
$$ \frac { x_1 - x_0 } { t } = v_0 + \frac { - v_0 } {2} $$
$$ \frac { 2 ( x_1 - x_0 ) } { t } = 2 v_0 - v_0 $$
$$ v_0 = \frac { 2 ( x_1 - x_0 ) } { t } $$ 
And put it back into equation for acceleration: 
$$ a = \frac { - v_0 } { t } $$
$$ a = \frac { - \frac { 2 ( x_1 - x_0 ) } { t } } { t } $$
$$ a = - \frac { 2 ( x_1 - x_0 ) } { t^2 } $$ 
So we got an acceleration that i need to apply to an object over a time interval $t$, so that it would stop at $x_1$ with velocity $0$, right? 
But it doesn't work! 
Because it doesn't depend on initial velocity at all! So if my object is flying at 2 m/s then i would need to apply the same acceleration as if it was flying 100 m/s, or 1000 m/s? How come? 
Where am i being wrong? This all seems mathematically sound... Am i setting the wrong premises? Interpreting results in the wrong way? 
I really need it for my project, and i've been trying to solve this for weeks, studying different aspects of maths that might help me, but i just can't do it :( 
But this looks so simple! And yet i just can't do it. 11 years of school seem so useless right now... 
Help please 

As one of the comments suggested, it is not possible for all time intervals $t$. I ignored the fixing of the time interval and solved the problem without that constraint. Hope it helps:
EDIT: If you want to still have a fixed $t_1$, you can view the obtained equation for $t_1$ as a constraint, that must hold, for the problem to have a solution.

Equations of motion of the object:
$$a(t) = a_0$$
$$v(t) = v_0 + a_0t$$
$$x(t) = x_0 + v_0t + \frac{a_0}{2}t^2$$

Equations that have to be satisfied:
$$x_1 = x_0 + v_0 \cdot t_1 + \frac{a_0}{2}t_1^2$$
$$v_1 = v_0 + a_0 \cdot t_1$$
Where $t_1$ is the time, when the object is at $x_1$, so $x(t_1) = x_1$
You have two unknowns: $a_0$ and $t_1$.
Proceeding as you described, you get: 
$$a_0 = -\frac{v_0}{t_1}$$
Plugging this into the first equation, that must be satisfied, gives:
$$x_1 = x_0 + v_0 \cdot t_1 + \frac{-\frac{v_0}{t_1}}{2}t_1^2$$
$$t_1 = \frac{2(x_1-x_0)}{v_0}$$
Plug this into the obtained equation for $a_0$:
$$a_0 = -v_0 \cdot \frac{v_0}{2(x_1-x_0)}$$
$$a_0 = - \frac{v_0^2}{2(x_1-x_0)}$$
