The speed of the automobile is given in km/h. We need to convert this to m/s.
130.0 km/h=130.0×1000 m1 km×1 h3600 s=36.1111 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} 130.0km/h=130.0×1km1000m×3600s1h=36.1111m/s
The kinetic energy K K K is given by the formula:
K=12mv2 K = \frac{1}{2} m v^2 K=21mv2
For the automobile:
K=12×2002.0 kg×(36.1111 m/s)2=1.305×106 J K = \frac{1}{2} \times 2002.0 \, \text{kg} \times (36.1111 \, \text{m/s})^2 = 1.305 \times 10^6 \, \text{J} K=21×2002.0kg×(36.1111m/s)2=1.305×106J
Using the same kinetic energy formula for the runner:
K=12×84 kg×(13 m/s)2=7107 J K = \frac{1}{2} \times 84 \, \text{kg} \times (13 \, \text{m/s})^2 = 7107 \, \text{J} K=21×84kg×(13m/s)2=7107J
Using the kinetic energy formula for the electron:
K=12×9.1×10−31 kg×(2.3×107 m/s)2=2.404×10−16 J 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} K=21×9.1×10−31kg×(2.3×107m/s)2=2.404×10−16J
(a) The kinetic energy of the automobile is 1.305×106 J\boxed{1.305 \times 10^6 \, \text{J}}1.305×106J.
(b) The kinetic energy of the runner is 7107 J\boxed{7107 \, \text{J}}7107J.
(c) The kinetic energy of the electron is 2.404×10−16 J\boxed{2.404 \times 10^{-16} \, \text{J}}2.404×10−16J.
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