M1 Kinematics: 2 solutions , which is correct?

In this question , the acceleration is worked out to be 0.34 ms^-2 in part a).

The problem is that in part b); to work out the total time taken for the car to travel to A to C; I used the suvat equation s=vt -0/5at^2, where s is the total distance; (100+300=400m), v is the final velocity when the car is at point C (20m/s) and acceleration as previously worked out is 0.34ms^-2. So all I have to do is work out t. However when using this suvat equation, I get two values of t; both are positive but only ONE is the right answer; which is 25.5s. (The other value is something like 94s). When using this equation, how could you possible know which one is the correct one, and thinking about it in terms of the question , how could there even be two possible times for the car travelling from A to C , because the car has a positive acceleration and only passes both points once, then accelerating off into the distance further away?

For your second value of t of 94s, the initial velocity is negative, and the car travels backwards from A, and comes to rest, and then starts moving forward, through A, to C.
Acceleration is constant throughout.

How have you deduced that the initial velocity is negative and the car travels backwards from A?