SERPSE$102.$C$.$P$.044.$CTX$.$

Review. You are sitting in your car at rest at a traffic light with a bicyclist at rest next to you in the adjoining bicycle lane, As soon as the traffic light turns green, your car speeds up from rest to $49\mathrm{.}0m\frac{i}{h}$ with constant acceleration $7\mathrm{.}00\frac{m}{h}\frac{?}{s}$ and thereafter moves with a constant speed of $49\mathrm{.}0m\frac{i}{h}.$ At the same time, the cyclist speeds up from rest to $23\mathrm{.}0\frac{m}{h}$ with constant acceleration $14\mathrm{.}00m\frac{i}{h}\frac{?}{s}$ and thereafter moves with a constant speed of $23\mathrm{.}0m\frac{i}{h}.$

$($a$)$ For what time interval $($in s$)$ after the light turned green is the bicycle ahead of your car?

Write equations for the positions of the car and blcycle as a function of time and set the positions equal to each other $s$

$($b$)$ What is the maximum distance $($in $ft)$ by which the bicycle leads your car during this time interval?