You stand sideways in a moving train. Estimate how far apart you should keep your feet so that when the train accelerates at 3.2 m/s2 you can still stand without holding anything. Let d be the distance of separation between your feet, and h = 0.90 m be the vertical distance between your center of mass and the floor.

d = 0.588 m

Explanation:

If we assume that each foot is of the same distance from the center of mass position

Let d be the separation between the two feet

The distance from one foot to the center of mass = d/2

Energy expended by the passenger due to each of the feet due to gravity

E = mgd/2 ... (1)

The force acting on the passenger due to the acceleration of the train and the height of the passenger from the center of mass

E = mah ... (2)

Equating (1) and (2)

mgd/2 = mah

d = 2ah/g

d = 2 * 3.2 * 0.9/9.8

d = 0.588 m