Btw; littleyellowcar you could have been thinking of Stoke's Law which is F = 6πrηv (not sure if that will all show up but it's Frictional force = 6*pi*r*velocity) for a spherical object.
That's frictional drag, F proportional to V for that.
However, there's also the Drag equation, something I didn't cover at A level but it is given as:
If that doesn't show it's:
D = 0.5Cd*ro*A*v^2
I.e. Drag = 0.5 * coeffieicnt of drag * density * Area (I expect the area facing it)*velocity squared.
Quite worrying this is on my sllyabus but we haven't covered it in my degree! Better go and learn about it!
Wikipedia has this to say about it:
Another interesting relation, though it is not part of the equation, is that the power needed to push an object through a fluid increases as the cube of the velocity. A car cruising on a highway at 50 mph (80 km/h) may require only 10 horsepower (7 kW) to overcome air drag, but that same car at 100 mph (160 km/h) requires 80 hp (60 kW). This is because the force exerted by drag quadruples (2² = 4), and the power required equals force times velocity.
So similar to as you said, increasing v has a large increase of drag force but as I wrote before, as we're talking 0-60 and not top speed this wouldn't cause a problem AFAIK.