What is the maximum sustained horizontal acceleration possible on a flat track in a motorcycle whose wheels are 2 m apart centre to centre, centre of mass symmetrically between the wheels and 0.5 m from the ground? Assume friction with the road is not limiting.

To determine the reaction on the front wheel, we do a momentum balance on the rear wheel aligned with the center of mass:

W (1) = W (0.5) (1) + R (0.5)

R = W

For the motorcycle to accelerate, there must imbalance of forces, so:

ma = R - F

since friction is not limiting:

ma = mg (1 - 0.5)

a = 0.5 g

Therefore, the acceleration is 0.5 g or 0.5 (9.81) = 4.91 m/s2