3.6 Exercise 4

Between t = 0 and t = t₀, a rocket moves straight upward with an acceleration given by $a \left(t\right) = A - B t^{1 / 2}$, where A and B are constants. (a) If x is in meters and t is in seconds, what are the units of A and B? (b) If the rocket starts from rest, how does the velocity vary between t = 0 and t = t₀? (c) If its initial position is zero, what is the rocket’s position as a function of time during this same time interval?