Questions: Calculate the kinetic energies (in J) of the following. (a) a 2,002.0 kg automobile moving at 130.0 km/h J (b) an 84 kg runner sprinting at 13 m/s J (c) a 9.1 x 10^-31 kg electron moving at 2.3 x 10^7 m/s J

Solution Steps

The speed of the automobile is given in km/h. We need to convert this to m/s.

\[ 130.0 \, \text{km/h} = 130.0 \times \frac{1000 \, \text{m}}{1 \, \text{km}} \times \frac{1 \, \text{h}}{3600 \, \text{s}} = 36.1111 \, \text{m/s} \]

The kinetic energy \( K \) is given by the formula:

\[ K = \frac{1}{2} m v^2 \]

For the automobile:

\[ K = \frac{1}{2} \times 2002.0 \, \text{kg} \times (36.1111 \, \text{m/s})^2 = 1.305 \times 10^6 \, \text{J} \]

Using the same kinetic energy formula for the runner:

\[ K = \frac{1}{2} \times 84 \, \text{kg} \times (13 \, \text{m/s})^2 = 7107 \, \text{J} \]

Using the kinetic energy formula for the electron:

\[ K = \frac{1}{2} \times 9.1 \times 10^{-31} \, \text{kg} \times (2.3 \times 10^7 \, \text{m/s})^2 = 2.404 \times 10^{-16} \, \text{J} \]

Final Answer