Should the Bus Driver Brake or Accelerate at the Orange Light?

[hazel31]

When the front a 5.0 m long bus traveling at a constant speed of 20 m/s is 55 m away from an intersection, the traffic light turns orange. It will take 3.0 s before the light turns red. The driver's reaction time is 0.25 s. The bus can accelerate up to 2.0 m/s/s or slows down at a maximum rate of 4.3m/s/s. The intersection is 22.0 m wide. Should the driver step on the brakes or on the gas pedal? (Young, 2000)

-- I'm confused there are too many given :(

 

[Hootenanny]

Welcome to Physics Forums.

When the front a 5.0 m long bus traveling at a constant speed of 20 m/s is 55 m away from an intersection, the traffic light turns orange. It will take 3.0 s before the light turns red. The driver's reaction time is 0.25 s. The bus can accelerate up to 2.0 m/s/s or slows down at a maximum rate of 4.3m/s/s. The intersection is 22.0 m wide. Should the driver step on the brakes or on the gas pedal? (Young, 2000)

-- I'm confused there are too many given :(

There are two scenarios to consider here: (a)The driver sees the amber light and decides to try and get through the intersection before the light turns red, or (b) Tries to stop before the light turns red.

So the important questions are: If the driver tries to get through the lights, will he make it? If the driver decides to try to stop, will he stop before the lights.

P.S. I responded to this thread before I had read your PM. Please do not send unsolicited requests for help via Personal Message.

 

[hazel31]

Welcome to Physics Forums.

There are two scenarios to consider here: (a)The driver sees the amber light and decides to try and get through the intersection before the light turns red, or (b) Tries to stop before the light turns red.

So the important questions are: If the driver tries to get through the lights, will he make it? If the driver decides to try to stop, will he stop before the lights.

P.S. I responded to this thread before I had read your PM. Please do not send unsolicited requests for help via Personal Message.

Thank You for your effort to give me a hint .. I'm sorry I am just new to this forum .. Sorry Again :(

 

[I like Serena]

Welcome to PF, hazel31!

Let's break this problem down into smaller pieces.

I'm starting with the smallest piece I can think of.
Suppose the bus driver steps on his brake immediately.
What will be his braking distance?

You will need his initial speed. What is it?
And you need the deceleration rate. What is it?
You also need a formula to calculate the corresponding braking distance.
Do you know what that formula is?

 

[rwisz]

I would approach this problem by breaking it down into smaller, more manageable parts. First, we need to determine the distance the bus will travel during the 3.0 seconds before the light turns red. This can be calculated by using the formula d = v0t + 1/2at^2, where d is the distance, v0 is the initial velocity, a is the acceleration, and t is time. In this case, v0 is 20 m/s, a is -4.3 m/s/s (since the bus is slowing down), and t is 3.0 seconds. This gives us a distance of 30.9 meters.

Next, we need to determine the distance the bus will travel during the driver's reaction time of 0.25 seconds. This can be calculated by using the same formula, but with a different value for t. In this case, t is 0.25 seconds, and all other values remain the same. This gives us a distance of 1.25 meters.

Now, we can determine the total distance the bus will travel before reaching the intersection by adding the two distances calculated above (30.9 + 1.25 = 32.15 meters). Since the intersection is only 22.0 meters wide, it is clear that the bus will not be able to stop in time if the driver steps on the gas pedal. Therefore, the driver should step on the brakes in order to safely stop the bus before reaching the intersection.

It is also important to note that these calculations assume ideal conditions and do not take into account factors such as reaction time variations, road conditions, and other variables that may affect the bus's stopping distance. It is always important for drivers to use caution and follow traffic laws to ensure the safety of themselves and others on the road.