Question

How much force is needed to accelerate a 55 kg cart at 15 m/s²

Answer 1

The procedure is the very same, the concept is that now the object is at rest and you have to APPLY the force.
If the object is in movement with the same values the force that carries is EXACTLY the same you need to put it in movement.

Answer 2

is the unit for force is Newton?
if it is then N = kg-m / s^2
means you just have to multiply the two givens 55 x 16

+not quite sure though