Question

acceleration of cart
multiple choice question
for the graph, acceleration of cart, various forces were applied and the acceleration measured. which statement must be true for the objects in the investigation that generated this graph?
o the objects with the large accelerations were smaller masses.
o the objects with the larger accelerations were larger masses.
o they were all of the same mass.
o no conclusion can be drawn with respect lot he masses of the objects.
need help? review these concept resources.
read about the concept

Explanation:

Step1: Recall Newton's second law

Newton's second law is \(F = ma\), where \(F\) is force, \(m\) is mass, and \(a\) is acceleration. Rearranged, \(m=\frac{F}{a}\).

Step2: Analyze the relationship between \(F\), \(a\), and \(m\)

If we consider the graph of \(F\) vs \(a\), for a given object (constant \(m\)), \(F\) and \(a\) are directly proportional (\(F = ma\)). But in this graph, when \(a\) is larger (smaller), \(F\) is smaller (larger). Since \(m=\frac{F}{a}\), a larger \(a\) for a smaller \(F\) implies a smaller \(m\), and a smaller \(a\) for a larger \(F\) implies a larger \(m\).

Answer:

The objects with the larger accelerations were larger masses.