An airplane starts from rest and accelerates at \( 12.6 \mathrm{~m} / \mathrm{s}^{2} \). What is its speed at the end of a 1790 m long runway? A. none of the above B. \( 34500 \mathrm{~m} / \mathrm{s} \) C. \( 131 \mathrm{~m} / \mathrm{s} \) D. \( 4320 \mathrm{~m} / \mathrm{s} \) E. \( 212 \mathrm{~m} / \mathrm{s} \)

To find the speed of the airplane at the end of the runway, we can use the kinematic equation: \[ v^2 = u^2 + 2as \] where: - \( v \) is the final speed, - \( u \) is the initial speed (0 in this case since it starts from rest), - \( a \) is the acceleration (\( 12.6 \, \mathrm{m/s^2} \)), - \( s \) is the distance traveled (\( 1790 \, \mathrm{m} \)). Plugging in the values, we get: \[ v^2 = 0 + 2 \cdot 12.6 \cdot 1790 \] Calculating that, we get: \[ v^2 = 2 \cdot 12.6 \cdot 1790 \approx 45072 \] Taking the square root gives us: \[ v \approx 212.3 \, \mathrm{m/s} \] So the closest answer is **E. \( 212 \mathrm{~m/s} \)**. Now, let's take a look at some fun facts! One fun fact is that the acceleration of an airplane during takeoff can often be quite similar to what you experience on a roller coaster. It's all about that thrilling rush as the plane speeds down the runway, ready to take flight! For the second tidbit, you might not know that the top speed for commercial jet aircraft is usually between 850 km/h and 950 km/h (about 530 to 590 mph), which can make you feel just how fast your favorite jets really are when compared to the speed you calculated here. That's quite the speed-up from the runway!