Sounds like the situation is modeled like so:
[Light] - - - - - - - - - - [You] => - - -
- - - - - - - - - - - - - - - [Cop] - - - - -
<= = = 200 m = = =>
where your velocity is 27.8 m/s to the right. So the question is asking, is it possible that your car, given that it accelerates at a maximum of 1/5 m/s^2, can reach a speed of 27.8 m/s from rest in the time it takes for it to cover 200 m.
The car's position at time [tex]t[/tex] is
[tex]x=\dfrac12\left(1.5\dfrac{\rm m}{\mathrm s^2}\right)t^2[/tex]
The time it takes to traverse 200 m is
[tex]200\,\mathrm m=\left(0.75\dfrac{\rm m}{\mathrm s^2}\right)t^2\implies t\approx16.3\,\mathrm s[/tex]
Your car's velocity at time [tex]t[/tex], starting from rest, is
[tex]v=\left(1.5\dfrac{\rm m}{\mathrm s^2}\right)t[/tex]
so that after 16.3 s, your car is moving at a speed of
[tex]v=\left(1.5\dfrac{\rm m}{\mathrm s^2}\right)\left(16.3\,\mathrm s\right)\approx24.5\dfrac{\rm m}{\rm s}[/tex]
which is less than the speed the cop claims you were going, so the cop is not correct.
