Distance of a particle; a function its time

Question

Force is a function of mass and acceleration. Here mass is a fundamental quantity, and acceleration is a derived quantity OR $F(a, m) = ma$.

I want to ask that why the distance traveled by a particle is only the function of $time$? While, $S = vt$. Where $S$ is the distance traveled, $v$ is the velocity and $t$ is the time. Why is it not a function of its velocity too? Here time is a fundamental quantity and velocity is a derived quantity as in the case of force. Also Force is directly proportional to mass as distance is directly proportional to time.

Answer 1

Given a particle trajectory then at each point in time the particle has traveled a precise distance, but given a certain value for velocity there may be more than one point on the particle's trajectory where the particle was traveling at that velocity, thus the velocity at a pont in the the trajectory does not determine the distance the particle has traveled. However, if the particle is traveling say with constant acceleration than this would be a case where the distance traveled is a function of velocity.

Answer 2

$$S(v, T)= \int_{0}^{T}v(t)dt$$ So really, distance is not proportional to time in general, and is proportional only if $v$ is a constant, i.e. $S=vt$ is only true if $v$ is constant.

$S$ is a function of $v$ and $T$.