Question

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?

Answer 1

Dear student,

Acceleration is linearly dependent.
$$\begin{gathered} Acceleration=ax+b \\ Acc=4,b=3forx=0. \\ Acc=0fora=-\raisebox{1ex}{$4$}\!\left/ \!\raisebox{-1ex}{$3$}\right.,b=3 \\ andAccelerationisa=v\frac{dv}{dx} \\ Onintergrating, \\ {\int }_0^{v}vdv={\int }_0^3\left(4-\frac{4x}{3}\right)dx \\ v=\sqrt{12}m/s \end{gathered}$$

Regards.