Velocity and Distance; Functions of Time

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$s(t)$ = distance a particle travels from time $0$ to $t$. If in this case, the distance $s$ is only the function of time then its necessary that the velocity should be constant. Likewise, $v(t)$ = velocity of a particle at time $t$, if in this case velocity is only the function of time then the distance traveled should be constant. Am I right?