Question

a student studies the effect of an objects speed on its amount of kinetic energy. this graph summarizes the data from the study. which statement best describes what the graph shows? a. as speed increases, kinetic energy stays the same. b. as kinetic energy increases, speed decreases exponentially. c. as speed increases, kinetic energy increases exponentially. d. as speed decreases, kinetic energy doubles each time.

Explanation:

Step1: Analyze the graph trend

The graph shows a curve that rises upwards as speed (x - axis) increases. This indicates a positive relationship between speed and kinetic energy.

Step2: Recall the kinetic energy formula

The formula for kinetic energy is \(K.E.=\frac{1}{2}mv^{2}\), where \(m\) is mass and \(v\) is speed. Since \(m\) is constant (assuming the mass of the object does not change), kinetic energy is proportional to the square of the speed (\(K.E.\propto v^{2}\)). A relationship of the form \(y = ax^{2}\) (where \(a=\frac{1}{2}m\)) is a quadratic (exponential - in the sense of polynomial degree 2) relationship.

Answer:

C. As speed increases, kinetic energy increases exponentially.