The derivative of `s=2t^2+3` is the same as the derivative of `y=2t^2`, namely `4t`. Geometrically this is clear since the graph of `s=2t^2+3` is just an upward translation of the graph of `y=2t`. In particular, at `t=1`, `2`, and `3` the derivative assumes the values `4`, `8`, and `12` respectively.