Get the minimum taken to move from A to B given a cap on Velocity

1. The problem statement, all variables and given/known data
Find the minimum time taken for the object to cover the distance x

I’m given the following:
x = the distance i need to cover
V0 = the initial velocity which is zero
a = the maximum permissible acceleration
Vmax = the maximum permissible velocity

2. Relevant equations

the speed of the object is (v0 + t * a) at time t
the object will be (v0 * t + 0.5 * a * t^2) away

3. The attempt at a solution

I used the kinematic equation x/2 = V0 + 0.5at^2 to find t. In some case this worked for example using the test case x = 1, a = 2, Vmax = 10 then t = 1.414…; x = 1, a = 1, Vmax = 1 then t = 2s
but for the case x = 10, a=1, Vmax = 1 I failed to get the correct answer (11 s). Would anyone here please help me understand how to account for Vmax and a. I’m not sure how the equations given in the problem statement aid in getting the answer. thanks

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