Question

Which graph shows the correct relationship between kinetic energy and speed? A. Graph representing the relationship between speed on the x-axis and kinetic energy on the y-axis. A straight line starts at the y-axis B. Graph representing the relationship between speed on the x-axis and kinetic energy on the y-axis. A straight line starts from the origin C. Graph representing the relationship between speed on the x-axis and kinetic energy on the y-axis. A curve line runs parallel to the x-axis and y-axis D. Graph representing a relationship between speed on the x-axis and kinetic energy on the y-axis. A semi-curve line starts above the origin on the y-axis and curves upwards as it moves forward in speed

Answer 1

The correct graph for the kinetic energy versus speed relationship is a parabolic curve starting from the origin, representing a quadratic relationship where kinetic energy is proportional to the square of the speed.

Step-by-step explanation:

The correct relationship between kinetic energy and speed is represented by a graph where kinetic energy is the dependent variable (on the y-axis) and speed is the independent variable (on the x-axis). The kinetic energy (KE) of an object is directly proportional to the square of its speed (v), that is, KE = 1/2 m*v2, where m is the mass of the object. Hence, the graph depicting this relationship should be a curve that gets steeper as the speed increases, matching option C which describes a curve that starts at the origin and curves upward as speed increases.

While a straight-line graph with the equation y = mx + b describes linear relations, in the case of kinetic energy versus speed, we are dealing with a quadratic relationship, which produces a curved graph. This is because the speed (v) is squared in the kinetic energy equation. The quadratic nature of the graph means that it starts at the origin (when speed is zero, kinetic energy is also zero) and as speed increases, the kinetic energy increases at an accelerating rate, creating a parabolic curve on the graph.