Problem Statement

The parameters for an electric vehicle are shown in the table below. $($a$)$ Determine the optimum cruising speed $($in kph$)$ to

minimize total energy usage for this vehicle during a fixed$-$distance journey.

The auxiliary systems power draw specifies the amount of power required to run auxiliary systems whether the vehicle is

moving or not. For this problem, rolling resistance should not be neglected. Also note that the "drag area" is the product of

the drag coefficient and the frontal area.

$($b$)$ Estimate the size of motor required $($in kW $)$ if the vehicle is to reach its optimum cruising speed within $250$ m $.$ Note

that the motor does not need to supply the auxiliary power, which is drawn directly from the batteries. You may also

neglect internal transmission$/$conversion losses and just determine the power provided by the drivetrain at the tire$/$road

interface.

Note: When presenting your work, it will be much easier for the audience to understand if you treat each part of the

problem separately $-$ so present the solution procedure, results, and validation for Part A before moving on to Part B$.($The

two parts of this problem are not closely related to each other.$)$

Validation

You should be able to solve Part A analytically. Show that your answer is a maximum point by using your

analytical solution to plot $E(V).$

If you are able to solve Part B analytically, use a numerical method to validate. If you resort to a numerical

method to obtain your primary solution, use an alternative method to validate.

Solve Part B while neglecting rolling resistance. This should make it easier to solve the problem analytically.

$($Your primary solution to part B should include rolling resistance.$)$