Graphing Instantaneous Power

The video tutorial explores the concept of instantaneous power delivered by gravity to a pumpkin dropped from a height. It examines whether the power as a function of time and position is linear. The tutorial uses physics equations to determine the linearity of these relationships, concluding that power as a function of time is linear, while power as a function of position requires squaring to achieve linearity. The session includes problem-solving and equation manipulation to illustrate these concepts.

What is the initial height from which the pumpkin is dropped?

• 8.53 meters

• 8.91 meters

• 9.81 meters

• 7.53 meters

Which equation is used to find the instantaneous velocity of the pumpkin in terms of time?

• v^2 = u^2 + 2as

• F = ma

• v = u + at

• s = ut + 0.5at^2

What is the slope of the power-time graph for the falling pumpkin?

• Mass times acceleration due to gravity

• Mass times height

• Mass times acceleration due to gravity squared

• Mass times velocity

Why is the power-position graph not linear?

• Because power is inversely proportional to position

• Because power is proportional to the square root of position

• Because power is proportional to the square of position

• Because power is directly proportional to position

What transformation is needed to make the power-position graph linear?

• Graph power against the square root of position

• Graph power squared against position

• Graph power against position squared

• Graph power against position

What is the slope of the linear graph when power squared is plotted against position?

• Mass squared times acceleration due to gravity

• Mass times acceleration due to gravity squared

• Negative 2 times mass squared times acceleration due to gravity cubed

• Negative 2 times mass times acceleration due to gravity

What is the approximate value of the slope when power squared is plotted against position?

• 821 kg*m^2/s^4

• 137,000 kg^2*m^4/s^6

• 1,100 watts

• 1.2 milliwatts squared