rush out (of something or some place)
1. To exit, escape, or depart (from something or some place) very quickly or all at once. People came rushing out of the burning building. He rushed out of the office to catch the last train home. I opened the lid of the saucepan and plume of steam rushed out.
2. To cause or direct someone or something to exit, escape, or depart (from something or some place) in a very hasty or frantic manner. In this usage, a noun or pronoun is used between "rush" and "out." The security guards rushed us out of the building after the first gunshot went off. After the machine caught fire in the lab, we rushed it out and sprayed it with a fire extinguisher. I hate having to rush the kids out in the morning, but they just take so long to get ready for school.