Math. 350-01, Fall, 2002, Illustration of Mathematica for Symbolic Solution and Plotting Solutions

sol1  =  
      DSolve[{v'[t]  -  (9.8 - v[t]/5)  == 0, v[0] == 0},  v[t], 
         t]

v1[t_]  =  Simplify[v[t]  /.  First[sol1]]

Plot[v1[t], {t, 0, 3.5}]

s[t_]  =  (∫_0^t) v1[u] \[DifferentialD]u

Solve[s[t] == 0, t]

FindRoot[s[t] == 300, {t, 5}]