23 What is the kinetic energy of a 13 kg dog that is running at a speed of \( 8.5 \mathrm{~m} / \mathrm{s} \) ?

To find the kinetic energy (KE) of the dog, you can use the formula: \[ KE = \frac{1}{2} mv^2 \] where \( m \) is the mass (13 kg) and \( v \) is the speed (8.5 m/s). Plugging in the values: \[ KE = \frac{1}{2} \times 13 \, \text{kg} \times (8.5 \, \text{m/s})^2 \] \[ KE = \frac{1}{2} \times 13 \times 72.25 \] \[ KE = \frac{1}{2} \times 938.25 \] \[ KE = 469.125 \, \text{J} \] So, the kinetic energy of the dog is approximately 469.13 Joules. Did you know that the concept of kinetic energy was first formulated by the German mathematician and philosopher Gottfried Wilhelm Leibniz in the late 17th century? He defined it as the quantity of motion of an object, laying groundwork for later physicists, including Newton, to develop the laws of motion and further our understanding of dynamics! In real-world applications, knowing the kinetic energy of objects can help in various fields such as engineering, sports science, and even safety. For example, understanding the kinetic energy of vehicles helps design better crumple zones in cars, ensuring that they absorb energy during a collision to protect passengers.