Question

About how much power does a sprinter produce if he transforms 2.70 kJ of chemical energy from food into kinetic energy and thermal energy in 14.0 seconds?

a) 192.9 W
b) 267.9 W
c) 385.7 W
d) 514.3 W

Answer 1

The formula for power (P) is given by:

\[ P = \frac{\text{Energy}}{\text{Time}} \]

Given that the energy transformed is \(2.70 \, \text{kJ}\) and the time is \(14.0 \, \text{seconds}\), you can substitute these values into the formula to find the power.

\[ P = \frac{2.70 \, \text{kJ}}{14.0 \, \text{s}} \]

First, convert kilojoules to joules (1 kJ = 1000 J):

\[ P = \frac{2.70 \, \text{kJ} \times 1000}{14.0 \, \text{s}} \]

Now, calculate the power:

\[ P = \frac{2700}{14.0} \, \text{W} \]

\[ P \approx 192.9 \, \text{W} \]

So, the answer is:

a) 192.9 W

Answer 2

The power output of a sprinter can be determined by calculating the rate at which they transform chemical energy into kinetic energy and thermal energy. In this case, the sprinter transforms 2.70 kJ of energy in 14.0 seconds, resulting in a power output of approximately 193 W.

Step-by-step explanation:

To determine the power output of a sprinter, we need to calculate the rate at which the sprinter transforms chemical energy from food into kinetic energy and thermal energy. Power is defined as the amount of work done or energy transferred per unit time. The formula to calculate power is:

Power = Energy / time

Given that the sprinter transforms 2.70 kJ of chemical energy in 14.0 seconds, we can substitute these values into the formula to calculate the power:

Power = 2.70 kJ / 14.0 s

Simplifying the calculation, we find that the sprinter's power output is approximately 0.193 kW, which is equivalent to 193 W.