Question $1\mathrm{.}3$ c and $1\mathrm{.}3d$

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

$v(t)=r[1-cos(st)]$

where values $r$ and $s$ are generated based on random parameters.

The starting time and position are both zero. The final time is given by $\frac{?}{\text{b}\text{a}\text{r}}(i{)}_{\text{e}\text{n}\text{d}},$ which is also randomily generated

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

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

Note that the timestep $dt$ is defined in the template

c$)$ Calculate an approximation to the final acceleration, a$\_$end$\_$approx, using a timestep $dt$ :Use the value$-$of the velocity at times $(I_{\text{m}\text{a}\text{d}}-dt)$ and $(I_{\text{e}\text{r}\text{d}}))$

d$)$ Calculate an approximation to the final displacement; $x\_$end$\_$approx, using the trapezium rule with time step $\frac{?}{\text{b}\text{a}\text{r}}(dt)=$

Script &