An airplane takes off on a runway that is 2 kilometers long. The plane starts off with an initial velocity of 5 meters/sec and moves with acceleration a(t)=a0+.1*t^0.75 (where a0 is a constant) for 45 seconds and then lifts off the end of the runway. How fast was the plane traveling (in meters/sec) on lift off? Model and solve using differential equations. Show all differential equations and all work.