The graphs of the acceleration as a function of mass and of the acceleration as a function of force are in attachment.
Explanation:
To answer both parts of the question, we refer to Newton's second law, which states that:
where
F is the net force on an object
m is the mass of the object
a is its acceleration
a)
To answer this part, we re-arrange the previous equation as follows:
Therefore, we notice that if a constant force is applied, the acceleration is inversely proportional to the mass of the object:
this means that if the mass increases, the acceleration decreases, and if the mass decreases, the acceleration increases.
In a graph of acceleration vs mass, the curve representing this relationship would be a hyperbole. The graph is shown as the first graph in the attached picture.
b)
As before, we re-arrange the previous equation as follows:
Here we notice that if the object has a constant mass, the acceleration is directly proportional to the force applied on the object:
this means that when the force increases, the acceleration increases, and when the force decreases, the acceleration decreases.
In a graph of acceleration vs force, the curve representing this relationship would be a straight line, as shown in the second graph in the attached picture.
Learn more about Newton's second law of motion here:
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