Please help me with this

Question

When a constant force acts upon an object, the acceleration of the object varies inversely with its mass. When a certain constant force acts upon an object with mass 4 kg, the acceleration of the object is 10 m/s^2. If the same force acts upon another object whose mass is 5 kg, what is this object's acceleration?

Answer 1

The acceleration varies inversely with its mass, so we define a proportionality constant k that will allow for us to write the inverse relationship as a = k/m. You can see that as m increases, a will decrease and vice versa for a constant k.

Using the condition that was given in the problem, we can determine k such that

k = a*m = (10 m/s^2) * (4 kg) = 40 kg*m/s^2 = 40 N

Knowing k, we can solve for the unknown acceleration when the mass is 5 kg:

a = k/m = (40 N) / (5 kg) = 8 m/s^2

This is an application and example of Newton's second law F = ma, hence the unit of Newtons (N) for the proportionality constant k.