Let's start with the force free body diagram
From Newton's laws we know:
thus:
where:
is engine power.
is the tyre rolling resistance coefficient.
And thus our equation is:
Now we know that terminal velocity happens when and ;
Which leaves us with
Now the reason why the vehicle mass does not effectively contribute to vehicle top speed is because of a car tyre the road surface is very small (in the 0.005 range), so the magnitude of the drag force at high velocities is much greater than of the friction force (can be over 10x more), hence it effectively becomes zero.
Therefore we are left with:
Or to rephrase it:
And so vehicle terminal velocity does not depend on power to weight ratio.