Question

A graph of an object’s kinetic energy is shown as a function of time over a 3-second interval. Which of the following conclusions about the object’s motion can be drawn from the graph? A. The work done on the object is 18 J.B. The impulse applied to the object is 18 N•s.C. The acceleration of the object is 4 m/s^2.D. The net force on the object is 4 N.E. The power delivered to the object is 4 W.Explain the graph rule that you used to answer this problem. Make sure to write the basic equation that represents the slope or area of the graph.

Answer 1

Notice that the K vs t graph passes through the point (0,0), which means that the initial kinetic energy was 0.

The kinetic energy increases linearly with time to reach 12J in 3s. The slope of a line is equal to the ratio of the change in the dependent variable over a change in the independent variable. In this case, the kinetic energy is the variable that depends on time. Then, the slope of the line is the ratio of a change in kinetic energy over a change in time.

The slope of a K vs t graph represents how fast the kinetic energy is transferred to the object. The magnitude that measures a change in energy over time is called Power.

Then, the slope of the graph (power delivered to the object) is:

`P=(\Delta\,K)/(\Delta\,t)=(12J)/(3s)=4(J)/(s)=4W`

Therefore, the correct choice is option E) The power delivered to the object is 4W.