Q21DQ - University Physics with Modern Physics

Question

Consider a graph of instantaneous power versus time, with the vertical P-axis starting at P = 0. What is the physical significance of the area under the P-versus-t curve between vertical lines at ${\mathbf{t}}_{\mathbf{1}}$ and ${\mathbf{t}}_{\mathbf{2}}$? How could you find the average power from the graph? Draw a P-versus-t curve that consists of two straight line sections and for which the peak power is equal to twice the average power.

Step-by-Step Solution

Answer

The average power is 3 W , and maximum power is 6 W.

The graph of the power vs time is shown as follows,

Step 1: Concept/Significance of kinetic energy

Kinetic energy is the power a thing possesses as a result of motion. As long as the system's kinetic energy is lower than its potential energy as a result of body contact, it stays bound.

Step 2: Determination of peak of power equal to twice the average power

The amount of work that external forces performed on an item between the instants and is what makes the region significant. The mean value theorem may be used to determine the average power as:

 

$P=\frac{{\int }_{t_1}^{t_2}P\left(t\right)dt}{t_2-t_1}$

 

The graph of the power vs time is shown as follows,

Thus, according to the graph, the average power is 3 W , and the maximum power is 6 W.