# A balloon is moving up from the ground in such a way that it's acceleration is linearly decreasing with its height above the ground. It starts from the ground with acceleration 4 m/S2 and with zero initial velocity. It's acceleration becomes zero at a height 3m. What is the speed of the balloon at a height 1.5 m?

Acceleration is linearly dependent.

$Acceleration=ax+b\phantom{\rule{0ex}{0ex}}Acc=4,b=3forx=0.\phantom{\rule{0ex}{0ex}}Acc=0fora=-\raisebox{1ex}{$4$}\!\left/ \!\raisebox{-1ex}{$3$}\right.,b=3\phantom{\rule{0ex}{0ex}}andAccelerationisa=v\frac{dv}{dx}\phantom{\rule{0ex}{0ex}}Onintergrating,\phantom{\rule{0ex}{0ex}}{\int}_{0}^{v}vdv={\int}_{0}^{3}\left(4-\frac{4x}{3}\right)dx\phantom{\rule{0ex}{0ex}}v=\sqrt{12}m/s$

Regards.

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