The speed of a vehicle is given by the following equation:

where values and are generated based on random parameters.

The starting time and position are both zero. The final time is given by $,$ which is also randomly generated.

A function file is built into this question to calculate the velocity at time $,$ such that it can be called using the following code:

$>>$ v $=$ velocity$($t$)$

Note that the timestep is defined in the template.

c$)$ Calculate an approximation to the final acceleration, a$\_$end$\_$approx, using a timestep $.$ Use the value of the velocity at times and $.$

d$)$ Calculate an approximation to the final displacement, x$\_$end$\_$approx, using the trapezium rule with time step $.$

$.$