Car acceleration problem

Hello there,

Just got an old car, and I was looking at the specifications, and trying to teach myself Newtonian physics. But I cannot get it to work out correctly. Please tell me where I go wrong.

The car weighs 900 kg. The engine has 200nm of torque, it accelerates from still to 27.7 m/s in 8 seconds. The radius from the center of the drive axle to the outside of the tire is circa 0.3m.

[itex]F = m\,a[/itex]

Assuming constant acceleration:

[itex]F = m\frac{v}{t}[/itex]

[itex]F = 900\mathrm{ kg}\frac{27.7\mathrm{ m/s}}{8\mathrm{ s}}[/itex]

[itex]F = 3116\,\mathrm{ N}[/itex]

So, to go from zero to 100km/h in 8 seconds takes 3116 N. This is not taking aerodynamic drag and drivetrain friction into account.

This is where I go wrong I think. The car has 200 Nm of torque:

[itex]\tau = 200\,\mathrm{Nm}[/itex]

I have an arm of 0.3m (the distance from the centre of the wheel to the outside of the tyre)

[itex]F = \frac{\tau}{r} [/itex]

[itex]F = 666 N [/itex]

The problem is [itex]3116\,\mathrm{ N} >> 666\,\mathrm{ N}[/itex]

And this is without even taken aerodynamic drag and drivetrain losses/friction and all of that jazz into account.

How come my maths is off by so much?

Thank you for your time.

Kind regards,
Marius

NOTE: Looks like my numbers may be off by a factor of 2∏ ? Not sure where it should go though.