1. In the mystical kingdom of Newtonia, a unicorn is using its horn to push a large stone of power across the icy ground towards the spot known as the Point of Destiny. 

The mass of the stone is 4600 kg, and the ground is perfectly level.  As the stone moves across the ground it experiences a constant resistance to movement of 3200 N. 

The unicorn’s horn, which may be modelled as a light rod, is held horizontal at all times.  While the unicorn’s magic would allow it to push with almost any force, the maximum thrust which the unicorn’s horn can withstand without shattering is 100 kN.

When the stone is exactly 100 metres away from the Point of Destiny and is being pushed at a speed of 1.8 metres per second, an evil wizard appears and begins to cast a spell of doom.  The spell will take exactly 3 seconds for the wizard to cast.

Given that the acceleration of the stone must remain constant over the entire 100 metre distance, and that the unicorn’s horn must not be allowed to shatter, determine whether or not the unicorn can get the stone to the Point of Destiny before the wizard completes his spell. 

Show complete mathematical workings to support your answer.