An airliner makes an emergency landing with its nose wheel locked in a position perpendicular to its normal rolling position. The forces acting to stop the airliner arise from friction due to the wheels and from the breaking effort of the engines in reverse thrust mode. The force of the engine on the plane is constant, Fengine = -F0. The sum of the horizontal forces on the airliner can be written as F(t)=-F0+(t/ts-1)*F1, from touchdown at time t=0s to the final stop time at ts=28s the mass of the plane is M=80tonnes, F0=254kN, F1=40kN Neglect all air drag and friction forces, except the one stated in the problem.

Question

a) Find the speed of the plain at touchdown
b) horizontal acceleration at time a(ts) a(0)
c) what distance s does the plane go between touchdown and the final stop time ts
d) What work do the engines during the reverese thrust mode during the landing
e) How much heat energy is absorbed by the wheels during the emergency landing?