IB Maths AI HL Sl 5 2 Increasing and Decreasing Functions Topic Practice

This question uses differential equations to model the maximum velocity of a skydiver in free fall.
In 2012, Felix Baumgartner jumped from a height of 40000 m . He was attempting to travel at the speed of sound, $330 \mathrm{~m} \mathrm{~s}^{-1}$, whilst free-falling to the Earth.
Before making his attempt, Felix used mathematical models to check how realistic his attempt would be. The simplest model he used suggests that

where $v \mathrm{~m} \mathrm{~s}^{-1}$ is Felix's velocity and $g \mathrm{~ms}^{-2}$ is the acceleration due to gravity. The time since he began to free-fall is t seconds and the displacement from his initial position is s metres.

Throughout this question, the direction towards the centre of the Earth is taken to be positive and v is a positive quantity.

When s=0, it is given that Felix jumps with an initial velocity v=10.

To test the model

Felix conducted a trial jump from a lower height, and data for v against t was found.

If the model is correct, describe the shape of the graph of v against t.

Felix's data are plotted on the following graph.