a particle starts moving from state of rest and it's velocity in t seconds is kt the distance travelled by it in t second is
See the velocity has the dimension of Distance/ Time. I.e., it states that how much distance a particle can travel with that velocity. Now the velocity kt means that the particle travels k distance per t seconds.
In t seconds the particle travels k unit of distance
Thus the distance travelled by the particle in t second is k unit of distance.
I hope this helps. Wish you a great eve!