Final answer:
The correct function formula for b(t) is b(t) = a(t), which is option (a) based on the provided information about the acceleration function and the kinematic equations governing motion. In this scenario, point B's distance from the wall varies directly according to the function a(t), with A and B having respective units of m/s^2 and (m/s^2)/s.
Step-by-step explanation:
To determine the correct function formula for b(t), which represents point B's distance from the wall in terms of the number of seconds t since the points were launched, given a function a(t), we must understand the given acceleration function and the kinematic equations governing the motion of objects.
The acceleration function a(t) = A - Bt1/2, where A and B are constants, indicates a time-dependent deceleration, with the units of A being meter per second squared (m/s2) and B having the units of (m/s2)/s. Given an initial velocity of zero, the velocity function v(t) would be integrated from the acceleration function, and the position function x(t) would be an additional integration of the velocity function.
Including the effects of the initial velocity and initial position, we can use the kinematic equation x = x0 + v0t + 1/2 a0t2 to represent the motion. In our case with a(t) = A - Bt1/2, there are no terms incorporating time t linearly in position function, thus b(t) = a(t), which corresponds to option (a), is the most likely correct formula for b(t). This indicates that point B's distance from the wall simply varies as per the function a(t), without additional adjustments for time or any other factors.