(1) solution: according to the meaning of the question, ob = 2oa = 5ad = 4op = t.

Because DA is perpendicular to the x axis

So OAD angle =90 degrees.

So the triangle is a right triangle.

So db 2 = ad 2+ab 2

Because AB=OA-OB=5-2=3.

So DB=5

Because DB=PC

So PC=5

Because DC is perpendicular to the y axis

So the angle OCD=90 degrees.

Because angle OAD+ angle AOC+ angle OCD+ angle ADC=360 degrees

Angle AOC=90 degrees

So the angle ADC=90 degrees.

Therefore, angle ADC= angle OAD= angle AOC= angle OCD=90 degrees.

So the quadrilateral OADC is a rectangle

So AD=OC=4.

Angle COP=90 degrees

So the triangle OPC is a right triangle.

So PC 2 = oc 2+op 2.

So t=OP=3.

So when t=3 seconds, DB=PC.

(2) Solution: Because PC is perpendicular to BC.

So BCP angle = OCB angle +OCP angle =90 degrees.

Because angle AOC+ angle OBC+ angle OCB= 180 degrees.

Angle AOC=90 degrees

So OBC angle +OCB angle =90 degrees.

So Angel ·OBC = Angel ·OCP

Because the angle AOC=COP=90 degrees

So the triangle OBC is similar to the triangle COP (AA).

So OC/OB=OP/OC

Because OC=4 OB=2

So t=OP=8.

So when t=8 seconds, PC is perpendicular to BC.

(3) Solution: Because the circle P is tangent to one side of the triangle BCD, let the tangent point be E and connect PE.

So the angle PEC=90 degrees

Because the quadrilateral OADC is a rectangle (proved)

So AD=OC=4.

Angle θc = angle POC = 90 degrees.

Because angle OCE+ angle POC+ angle PEC+ angle OPE=360 degrees.

So the angle OPE=90 degrees.

So angle OCE= angle POC= angle PEC=OPE=90 degrees.

So the quadrilateral Organization of Petroleum Exporting Countries is a rectangle.

Because PO=PE

So the quadrilateral organization of petroleum exporting countries is a square.

So OP=OC=4.

So t=4

So when t=4 seconds, the circle with P as the center and OP as the radius is tangent to the straight line on one side of the triangle BCD.