What is Kinetic energy?

Example 9.3 (Car versus pedestrian)

A $1300\,\mathrm{kg}$ car at $100\,\mathrm{km}/\mathrm{h}$ $= 27.8\,\mathrm{m}/\mathrm{s}$ carries $E_k = \tfrac12 \times 1300 \times 27.8^2 \approx 5.0 \times 10^{5}\,\mathrm{J}$; a $70\,\mathrm{kg}$ pedestrian at $1.5\,\mathrm{m}/\mathrm{s}$, $\tfrac12 \times 70 \times 1.5^2 \approx 79\,\mathrm{J}$ — six thousand times less. Speed is expensive: the square sees to it.

Example 9.5 (Water tower)

Each cubic metre ($1000\,\mathrm{kg}$) of water stored $30\,\mathrm{m}$ up a water tower holds $1000 \times 9.81 \times 30 \approx 2.9 \times 10^{5}\,\mathrm{J}$ — about six tenths of the car’s kinetic energy above. Cities stockpile energy overhead.

Example 18.2 (Orders of magnitude)

• a pedestrian, $70\,\mathrm{kg}$ at $1.4\,\mathrm{m}/\mathrm{s}$: $E_k = \tfrac12 \times 70 \times 1.4^2 \approx 69\,\mathrm{J}$;
• a car, $1300\,\mathrm{kg}$ at $130\,\mathrm{km}/\mathrm{h}$ $= 36.1\,\mathrm{m}/\mathrm{s}$: $E_k \approx 8.5 \times 10^{5}\,\mathrm{J}$;
• a high-speed train, $m = 3.85 \times 10^{5}\,\mathrm{kg}$, at $320\,\mathrm{km}/\mathrm{h}$ $= 88.9\,\mathrm{m}/\mathrm{s}$: $E_k \approx 1.5 \times 10^{9}\,\mathrm{J}$;
• a rifle bullet, $8.0\,\mathrm{g}$ at $800\,\mathrm{m}/\mathrm{s}$: $E_k \approx 2.6\,\mathrm{kJ}$.

Seven orders of magnitude separate the stroll from the train. And $E_k$ grows like the square of the speed: at $130\,\mathrm{km}/\mathrm{h}$ the car carries $4$ times the energy it has at $65\,\mathrm{km}/\mathrm{h}$ — four times what its brakes must remove.