A typical doughnut contains 2.0 g of protein, 17.0 g of carbohydrates, and7.0 g of fat. Average food energy values are 4.0 kcal/g for protein andcarbohydrates and 9.0 kcal/g for fat. (a) During heavy exercise, anaverage person uses energy at a rate of 510 kcal/h. How long would you have to exercise to “work off” one doughnut? (b) If the energy in the doughnut could somehow be converted into the kinetic energy of your body as a whole, how fast could you move after eating the doughnut? Take your mass to be 60 kg, and express your answer in m/s and in km/h.

Values listed in question are,

No. of grams of protein in a doughnut is 2.0 g

No. of grams of carbohydrate in a doughnut is 17.0 g .

No. of grams of fat in a doughnut is 7.0 g .

Energy value of protein is 4.0 kcal/g .

Energy value of carbohydrate is 9.0 kcal/g .

Energy rate during workout of a person is 510 kcal/h.

Kinetic energy is the energy a body possesses because of its state of motion. In order to provide a body at rest with some prescribed velocity work needs to be done to start the acceleration and this work is manifested in the body as its kinetic energy.

Mathematically,

$\mathbf{K}\mathbf{=}\frac{\mathbf{1}}{\mathbf{2}}{\mathbf{mv}}^{\mathbf{2}}$ ...(i)

Here, m is the mass of an object and v is its velocity.

The total energy content of doughnut is,

$\left(2.0\mathrm{g}\right)\left(4.0\mathrm{kcal}/\mathrm{g}\right)+\left(17.0\mathrm{g}\right)\left(4.0\mathrm{kcal}/\mathrm{g}\right)+\left(7.0\mathrm{g}\right)\left(9.0\mathrm{kcal}/\mathrm{g}\right)=139\mathrm{kcal}$

Thus, the time required is,

$$\begin{gathered} \frac{\left(139\mathrm{kcal}\right)}{\left(510\mathrm{kcal}/\mathrm{h}\right)}=0.273\mathrm{h} \\ =16.4\min \end{gathered}$$

The expression for speed from the equation (i),

$v=\sqrt{\frac{2\mathrm{K}}{\mathrm{m}}}$

For the given values above equation becomes,

$$\begin{gathered} v=\sqrt{\frac{2\left(139\times {10}^3\mathrm{cal}\right)\left(4.186\mathrm{J}/\mathrm{cal}\right)}{60\mathrm{kg}}} \\ =139\mathrm{m}/\mathrm{s} \\ =501\mathrm{km}/\mathrm{h} \end{gathered}$$

Thus the speed with which a person can move after having a doughnut is 501km/h.