After John passes the intersection, he accelerates and is clocked by a police officer at $45$

$mph,$ while the posted speed limit is $30mph.$ As he approaches a $40-$foot$-$wide signalized intersection,

the traffic light turns yellow when the front end of his vehicle is $250$ feet away from the intersection,

and then the light turns red $5$ seconds later.

a$.$ Can he stop in time? Explain. Assume a $1-$second perception$-$reaction time and a braking

deceleration rate of $11\mathrm{.}2f\frac{t}{s^2}.$

b$.$ Is there a dilemma zone for a $16-$foot$-$long passenger car traveling at the posted speed limit$,$

assuming the same perception$-$reaction time and deceleration rate? $($Assume acceleration rate $=0)$