When a valve is opened, fluid flows in the expansion duct of Fig. P4.8 according to the

Question:

When a valve is opened, fluid flows in the expansion duct of Fig. P4.8 according to the approximation
v = iU (1-x/2L) tanh Ut/L
Find (a) the fluid acceleration at (x, t) = (L, L/U) and (b) the time for which the fluid acceleration at x = L is zero. Why does the fluid acceleration become negative after condition (b)?

When a valve is opened, fluid flows