How fast did the first motcross bike go?

Answer 1

That's hard to answer because I'm not sure what one would consider to be the first Motocross bike.

There has been off road competition about as long as there has been motorcycles, but if I had to guess any organized racing resembling motocross started shortly after WW2.

But they used converted street bikes back then, English twins and singles. As such I imagine a bike could go 80mph quite easy, maybe only 60 or so on the fastest straights on the tracks though.

As dedicated smaller 2 stroke MX bikes were on the market in the early 60's on I am sure 60mph is a good figure. A bit faster if one geared them up for dessert racing, but right out of the box, I'd say one would really be screaming at 60 with the stock low gearing.