Question

A constant force $\mathbf{P}$ is applied to a piston and rod of total mass $m$ to make them move in a cylinder filled with oil. As the piston moves, the oil is forced through orifices in the piston and exerts on the piston a force of magnitude $k v$ in a direction opposite to the motion of the piston. Knowing that the piston starts from rest at $t=0$ and $x=0,$ show that the equation relating $x, v,$ and $t,$ where $x$ is the distance traveled by the piston and $v$ is the speed of the piston, is linear in each of these variables.

          A constant force $\mathbf{P}$ is applied to a piston and rod of total mass $m$ to make them move in a cylinder filled with oil. As the piston moves,
the oil is forced through orifices in the piston and exerts on the
piston a force of magnitude $k v$ in a direction opposite to the motion
of the piston. Knowing that the piston starts from rest at $t=0$ and
$x=0,$ show that the equation relating $x, v,$ and $t,$ where $x$ is the
distance traveled by the piston and $v$ is the speed of the piston, is linear in each of these variables.

Added by Melinda P.

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