Physics problems should be solved from first principles
In[8]:= xsoln[t_] =
DSolveValue[{x''[t] == -a, x'[0] == 29, x[0] == 0}, x[t], t]
Out[8]= 1/2 (58 t - a t^2)
In[10]:= Solve[{xsoln[tf] == 71, xsoln'[tf] == 0}, {a, tf}]
Out[10]= {{a -> 841/142, tf -> 142/29}}
In[11]:= N[%]
Out[11]= {{a -> 5.92254, tf -> 4.89655}}
