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Try this one out. I won't say that it is tough. Just requires your basics to be good. In fact, it is somewhat easy I would say.
A block of mass m is pulled with a constant force of magnitude mg/2 along a horizontal surface (assume it to be smooth). The force makes an angle with the horizontal which varies as = as where s is the displacement of the block and a is some constant. Find the velocity of the block, as a function of the angle at any instant that the force makes with the block.
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