A, the power is constant, the speed decreases, and according to P=Fv, the traction increases, so A is wrong;

B, when the car is driving at a constant speed v0, the traction is equal to the resistance, that is, F=f, the power of the engine is p, from P=Fv0=fv0, and the resistance is f = pv0.

When t=0, the power is half of the original, and the speed has not changed, then f = p2v0 = p2v0, according to Newton's second law:

a=F？ fm=？ P2mV0, so the size is P2mV0, so B is wrong.

According to the kinetic energy theorem, c and d: 0.5pt1+wf =12m (0.5v0) 2? 12mv02，

The work done by the resistor is wf =-38mv02-P2T1;

Let the displacement of the car pass by be X, which is obtained by Wf=-fx, and X = V0T 12+3mV038p. So, C is wrong and D is right.

So choose: D.