I'm glad to hear you drew the full Free-Body Diagram. (Few do!) The vertical forces, of course, do nothing here since implies , but it's a good habit to always quickly check this.

When in doubt use Newton's 2nd. Here it is simple, since there is only one horizontal force. So implies = 100 N/2 kg = 50 m/s^2.

So we know that the particle starts from rest and has an acceleration of 50 m/s^2 and moves for 10 m. (For the record I am setting up a +x direction to be in the direction of the acceleration and an origin to be at the point where the particle was at rest.)

The quickest equation to use would be:

Or t = 0.63 s to 2 significant figures.

-Dan