the speed of a train increases at a constant rate (alpha) from zero to v and then remains constant for an interval and finally decreses to zero at a constant rate(beta).the total distance travelled by the train is L.the time taken to complete the journey is t.then t is minimum value when v equals to?

I feel question is asking for min. value of t, what is value of v?

Then ans is 0. Time will be min when body starts the motion i.e its initial velocity is asked.

Plz. do point out my error,if any.

Plz. approve my answer if it is right.

sorry the answer isnt right.the right answer is root over 2L(ALPHA)(BETA) DIVIDED BY ALPHA+BETA. i need the explaination of the answer