Final answer:
The question is misstated, as the velocity function provided does not correspond to the given position function. Normally, one would differentiate the position function x(t) to find the particle's velocity v(t) over time in a calculus context.
Step-by-step explanation:
The subject of this question is Mathematics, specifically dealing with calculus and particle motion along the x-axis. The goal is to find the velocity of a particle over time when its position function x(t) is given. To find the velocity, we differentiate the position function x(t) with respect to time, given that the velocity function v(t) is the first derivative of the position function x(t).
However, the student is asking to show that v(t) = 70t / (3t² + 8)², which does not seem to be related to the provided function. This appears to be a typo or mistake. If we had the correct position function, we would differentiate it and possibly simplify it to obtain the velocity function. This process involves applying the rules of differentiation to the terms in the expression for x(t).