Hello,
Although throwing up, vomiting and nausea are the frequent symptoms in the first trimester but these symptoms can persist in some women in the second trimester also. If the vomiting are severe then hyperemesis gravidarum should be ruled out.
I hope it helps. Take care and regards.
From what I read on Medhelp and google, Its VERY normal. The perks of being pregnant. :] Its very common.