Given,
Distance should not exceed 165 ft.
So d(v) <= 165,
d(v) = v + (v^2 /25) <= 165
=> 25v + v^2 <= 165 * 25
=> v^2 +25v - 4125 <=0
On solving above quadratic equation we get,
1/2 (-25 - 5 sqrt(685))<=v<=1/2 (5 sqrt(685) - 25)
or
-77.93 <= v <= 52.93
but since velocity is assumed to be non-negative.
Therefore,
0 <= v <= 52.93