Smoothing an array/curve based animation

Hi, I’ve been following this blendercookie tutorial,

What I’m trying to do is, animate/keyframe the scaling of the path curve so that the plane grows and stretches around and stuff.

The problem is, when I animate/keyframe the scaling of the path curve, the growing plane doesn’t look very smooth (not the texture but the animation). What I mean is, it’s too segment-ish looking as it grows. Very quickly, you can see the plane grow segment by segment, I want it to flow more elegantly.

I’ve tried giving it vector handles and motion blur but it’s still animates blockishly looking. Here’s what I mean…