Answer to Question #233809 in Physics for Sean

Question

When the front of a 5 m long bus traveling at constant speed of 20 m/s is 55 m away from an intersection, the traffic light turns yellow. It will take 3 s before the traffic light turns red. The driver’s reaction time is 0.25 s. The bus can accelerate up to 2 m/s2 or slow down at a maximum rate of 4.3m/s2. The intersection is 22 m wide. Figure out whether the driver should step on the brakes or gas pedal by getting the total distance covered when they accelerate and when they slow down. 

Answer 1

Stopping distance

$$d=\frac{20^2}{2(4.3)}=46.51\ m$$

Distance through intersection

$$D=55+22+5=82\ m$$

$$s=20(3-0.25)+0.5(2)(3-0.25)^2=62.6\ m$$

Therefore, the driver must step on the brakes; because he or she cannot drive

the required 82 meters in 2.75 s.