For a train to come to a halt safely, it always passes a signal with a yellow light before it reaches a signal with a red light. At the yellow light, the driver applies the brake, and the train then undergoes a steady deceleration so that it stops exactly at the red light. The separation between the red and yellow lights is $x$. What is the smallest distance between the lights if the train speed is increased by $20\%$, while the deceleration of the trains remains unchanged?
- A$1.20x$
- B$1.25x$
- C$1.44x$
- D$1.56x$