Question

which graph shows the relationship between the mass of an object and the kinetic energy of an object when speed is constant?

Explanation:

Step1: Recall the kinetic energy formula

The formula for kinetic energy is \(K.E.=\frac{1}{2}mv^{2}\). When speed \(v\) is constant, \(K.E.\) is directly proportional to mass \(m\) (\(K.E.=(\frac{1}{2}v^{2})m\), where \(\frac{1}{2}v^{2}\) is a constant). A direct - proportional relationship between two variables \(y\) (kinetic energy) and \(x\) (mass) has the form \(y = kx\) (\(k=\frac{1}{2}v^{2}\) in this case), and its graph is a straight - line passing through the origin.

Step2: Analyze the graphs

• Graphs A and B have speed on the \(x\) - axis, but the question is about the relationship between mass and kinetic energy. So, A and B are incorrect.
• For graph C, as mass \(m\) increases, kinetic energy \(K.E.\) increases in a linear fashion (since the points seem to follow a straight - line trend which is characteristic of a direct proportion \(y = kx\)).
• Graph D does not show a linear relationship (the increase in kinetic energy with respect to mass is not consistent with a direct proportion).

Answer:

C