I am trying to represent two cars approaching an intersection where one car is traveling from a negative point along the x axis and another car is traveling from a negative point up the y-axis.
I have one car whose position is determined by the following:
$$x_1(t) = x_0+v_1*t+1/2*a_1*t^2$$ $$y_1(t) = 0$$
And another car whose position is determined by:
$$x_2(t) = 0$$ $$y_2(t) = y_0+v_2*t+1/2*a_2*t^2$$
How do I tell if there exists a time t for which these two cars collide at the origin with respect to the variables given?
You need to solve the system $$x_1(t)=y_2(t)=0.$$
For convenience, you can form the equation
$$a_2x_1(t)-a_1x_2(t)=0$$ which is linear in $t$.
After finding $t$, plug in the system and check if that $t$ matches.