Laplace transform of $$\cos \left( {\omega t} \right)$$ is

The Laplace transform of $${e^{i5t}}$$ where $$i = \sqrt { - 1} ,$$

A small ball of mass 1 kg moving with a velocity of 12 m/s undergoes a direct central impact with a stationary ball of mass 2 kg. The impact is perfectly elastic. The speed (in m/s) of 2 kg mass ball after the impact will be ____________

The initial velocity of an object is $$40$$ $$m/s.$$ The acceleration a of the object is given by the following expression: a$$=-0.1v$$
Where v is the instantaneous velocity of the object. The velocity of the object after $$3$$ seconds will be _______