How do you compare the acceleration of an object with gravity? or, how to express it as a multiply of gravity?

the problem i'm working with is this: an airplane accelerates at takeoff to a speed of 200km/hr in 18seconds. What is its acceleration compared to that of gravity? that is, find the acceleration in meters per second squared and express it as a multiply of g (gravity).





this is a problem in our physics 12 class.





help!How do you compare the acceleration of an object with gravity? or, how to express it as a multiply of gravity?
You need to bring the km/hr to meter/second.





velocity = 200 * 5/18 = 55.56 m/s





final velocity = initial velocity + acceleration * time





55.56 = acceleration * 18 (because initial velocity = 0)


acceleration = 55.56 / 18 = 3.086 m/s虏





Now usually g = 9.81 m/s虏. Your airplane's acceleration is 3.086 / 9.81 = 0.314 times that due to gravity.





(Curiously, that is about a 10th of the value of pi - 蟺 )How do you compare the acceleration of an object with gravity? or, how to express it as a multiply of gravity?
First off, let's convert 200km/hr to m/s so as to use standard S.I. units:


U = 200 km/hr = 200000 m / hr


now, an hour has 60*60=3600 seconds, so, finally:


U = 200000 / 3600 = 55.56 m/s


Now, assuming a constant acceleration, we have


U = Uo + a*t, therefore in your case:


55,56 = 0 + a*18 (since the aircraft was initially immobile)


That gives us a=55.56/18 = 3,1 m/sec^2 (approx)


and since the acceleration of gravity is g=9.81 m/s^2, your aircraft accelerates at about 3,1/9.81 = about 1/3rd of g.


(if you want to be exact it,s 0,315g)