2. Because point N moves along AB at a uniform speed of 5t, the coordinate of point N can be (6-3t, 4t). According to the problem, if the triangle BNP is a right triangle and the triangle ANM is also a right triangle, then the triangle ANM and the triangle AOB are similar triangles, and AN/AO=AM/AB can be obtained. The equation is 5t/6=6/ 10.

3. When BNP is an isosceles triangle and ANM is an isosceles triangle, then AN=MN and the equation is 5t=√[(6-3t+4-2t)? +(4t)？ ], solve the equation, t=5 or 5/4, t=5 is not the meaning of the question, so t=5/4 meets the meaning of the question.