Final answer:
The object's initial acceleration toward Earth is 5 m/s², calculated using Newton's second law a = F/m with the given weight and mass.
Step-by-step explanation:
When at a certain distance from the center of the Earth, a 0.4-kg object has a weight of 2.0 N, we can determine its initial acceleration upon release by using Newton's second law of motion. This law states that the acceleration (a) of an object is directly proportional to the net force (F) acting on it and inversely proportional to its mass (m), described by the formula a = F/m. Given the weight of the object (which is the force due to gravity) is 2.0 N, and the mass is 0.4 kg, we can calculate the acceleration as follows:
a = F/m = (2.0 N) / (0.4 kg) = 5 m/s²
The initial acceleration of the object towards Earth would then be 5 m/s². It is important to remember that this acceleration value would change if the object's location changes significantly, as the acceleration due to gravity varies slightly over the surface of the Earth and drastically in other celestial bodies such as the Moon.