Energy-height graph of a ball falling through a viscous fluid

[tatata]

Homework Statement

A ball falls from rest through a viscous fluid in a tall beaker of height H. It reaches terminal velocity at height H/2. Draw the energy-time graph for kinetic energy and gravitational potential energy on the same axes.

Homework Equations

F=6πηrv

The Attempt at a Solution

The graph of GPE should be a straight line with a negative gradient, cutting the y-axis at mgh and the x-axis at H.

The graph of KE should start from 0, then curve upwards before plateauing at H/2.
The problem is the shape of the curve before H/2. My teacher says that the graph should be concave upwards for H<1, then convex until H/2, meaning there is a point of inflection at H=1.

I think this is rather strange as the v-t graph is convex all the way until terminal velocity is attained. KE is 1/2mv^2, so shouldn't the graph be a straight line, if not convex all the way?

 

[tatata]

The problem statement should read "Draw the energy-HEIGHT graph for kinetic energy and gravitational potential energy on the same axes."