03 How do we measure the speed of a rocket? 10 Points It's difficult to measure the velocity of an object in empty space {after all, inside of a spaceship you do not feel that you are moving, even if you are traveling extremely quickly relative to the earth!). However it is easy to measure acceleration: that is the force that pushes you back into your seat when you push down on the gas pedal, or turn on a rocket engine. So, it is easy to equip a spaceship with acceleration sensors (even your cellphone has small accelerometers within to measure how you are holding it, for example), and it is useful to be able to do some data processing to the acceleration data to determine the velocity: that way we get the number we are interested in by only using things that are easy to measure! Recall that when acceleration is constant it is easy to determine how much a given acceleration changes velocity: if you are going at velocity U initially but then accelerate with constant acceleration a for 73 seconds, at the end of this time you'll be going at velocity "U l at. The complication is of course, that in the real world things rarely accelerate at a constant rate. The plot below shows the acceleration ofthe space shuttle during liftoff in its 12lst mission. Here you can see that the acceleration varies wildly, overtime, as the spacecraft turns on and off different engines. Mission Elapsed Time (MET) vs. Acceleration 35 30 P 25 20 Acceleration (m/s') 15 P2 10 P5 50 120 180 240 300 360 420 480 540 ABC-+DO E F . G Mission Elapsed Time (sec) GitHub Desktop Graph 1: Acceleration profile of STS 121 during the ascent phase. If, at t = 0 the space shuttle started out at rest, use the fundamental strategy of calculus to help you figure out a good estimate of what the final velocity of the space shuttle was after it got to orbit. Note: each box along the x-axis is 10sec long, and along the y-axis is 1m/s^2 tall. Explain all your thinking, and show your work This problem is an estimation problem; so I am not looking for an exact answer by any means: I am looking for a well explained and reasonable way to estimate the answer, and then a successful carrying out of that estimate