A train descending a $2\mathrm{.}0$ percent grade at $40m\frac{i}{h}r$ applies the brakes at $t=0.$

If the friction factor that is developed is $0\mathrm{.}05,$ then find:

$($a$)$ The speed of the train after it has traveled $1,000ft.$

$($Note: distances along the track and along its horizontal projection are

virtually the same because of the small angle.$)$

$($b$)$ The elapsed time after the train has traveled $1000ft.$