`v=int a\ dt`

So

`v=int(-20\ dt)/((1+2t)^2)`

Put `u = 1 + 2t` then `du = 2\ dt`, so `dt=(du)/2`

`v=int (-10\ du)/(u^2)`

`=int -10u^(-2)du`

`=10/u+K`

`=(10)/(1+2t)+K`

When `t = 0`, `v = 30`, so `K = 20`.

So the expression for velocity as a function of time is:

`v=((10)/(1+2t)+20)\ text[cm s]^-1`