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A body dropped from a very large height, experiences resistance to its motion due to air and has a varying acceleration which decreases to zero in time $$t$$. Assume the displacement in this time and the velocity acquired at the end of this time are same as that due uniform acceleration of $$cg$$ ($$c$$ is a constant less than 1). The body then travels with a uniform speed acquired at the end of time $$t$$. Find the displacement of the body in time $$2t$$.
Correct Answer: 0
PLACEHOLDER ANSWER - the answer is an expression. In the first interval the displacement is $$\frac{1}{2}cgt^2$$ and the velocity reached is $$cgt$$. In the next interval of length $$t$$ it moves uniformly at $$cgt$$, covering $$cgt^2$$. The total displacement in time $$2t$$ is $$\frac{1}{2}cgt^2 + cgt^2 = \frac{3}{2}cgt^2$$.
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