Problem $2$:

a$)$ A driver approaches an intersection with $25$ ft cross street widths at the posted

speed limit of $40$ mph $.$ Assuming a driver reaction time of $1\mathrm{.}0$ second and a deceleration rate of

$10$ft$/$sec$^(2),$ what is the red clearance interval required for the driver to clear the intersection?

b$)$ A signalized intersection approach has an upgrade of $4\%.$ The total width of the cross street at

this intersection is $60$ ft $.$ The average vehicle length is $16$ ft $.$ Assume drivers have a reaction

time of $1\mathrm{.}0$ seconds and a deceleration rate of $10$ft$/$sec$^(2).$ The speed of approaching traffic is

$40$ mph$.$ What is the sum of the minimum necessary change and clearance intervals?