Answer
Either strategy works.
Work Step by Step
We can convert $55~km/h$ to units of $m/s$:
$(55~km/h)\times (\frac{1000~m}{1~km})\times (\frac{1~h}{3600~s}) = 15.28~m/s$
We can find the distance we would travel without braking in a time of $2.8~s$:
$x = (15.28~m/s)(2.8~s) = 42.8~m$
Since the distance to the intersection is only $40~m$, we can continue driving at a constant speed of $55~km/h$
We can consider the situation if we decide to brake.
We can find the distance we travel in the $0.75~s$ before we react and apply the brake:
$x = (15.28~m/s)(0.75~s) = 11.46~m$
We can find the distance required to stop after we apply the brake and decelerate:
$v^2 = v_0^2+2ax$
$x = \frac{v^2 - v_0^2}{2a}$
$x = \frac{(0)^2 - (15.28~m/s)^2}{(2)(-5.18~m/s^2)}$
$x = 22.54~m$
After the light turns yellow, the total distance required to stop if we decide to apply the brake is $34~m$
Since the distance to the intersection is $40~m$, we can brake safely before reaching the intersection.
Therefore, either strategy works.
