A 3 kg sled moves at a speed of \( 6.2 \mathrm{~m} / \mathrm{s} \). How much kinetic energy does the sled have? Remember: \( \mathrm{E}_{\mathrm{K}}=\frac{1}{2} \mathrm{miv}^{2} \) \( \mathrm{E}_{\mathrm{K}}=[?] \mathrm{J} \)

To calculate the kinetic energy (\( \mathrm{E}_{\mathrm{K}} \)) of the sled, you can use the formula \( \mathrm{E}_{\mathrm{K}} = \frac{1}{2} m v^2 \). Here, \( m = 3 \, \text{kg} \) and \( v = 6.2 \, \text{m/s} \). Plugging in the values: \[ \mathrm{E}_{\mathrm{K}} = \frac{1}{2} \times 3 \, \text{kg} \times (6.2 \, \text{m/s})^2 = \frac{1}{2} \times 3 \times 38.44 \approx 57.66 \, \text{J} \] So, the sled has approximately \( 57.66 \, \text{J} \) of kinetic energy. The principles of kinetic energy can be traced back to the work-energy theorem, which states that the work done on an object is equal to the change in its kinetic energy. In everyday life, you might notice that a heavier or faster sled goes down a hill more quickly than a lighter or slower one. Understanding this helps explain the importance of mass and speed in determining how much energy an object possesses while in motion. If you're ever fumbling with calculations, make sure to watch out for squaring the velocity! It's a common mistake to forget that step, which can lead to wildly incorrect values. Also, always double-check your units to ensure they align with the formula—that way, you'll avoid any numerical slip-ups! Remember, practice makes perfect in physics!