# Solve Retardation Problem: 25m from Traffic Light

• takando12
In summary, the driver applies brakes when approaching a traffic light 400 m ahead while moving at 15m/s and retarding at a rate of 0.3m/s^2. After 1 minute, the distance of the vehicle from the traffic light is 25m. However, using a more accurate model, the distance is actually 40m as the driver does not reverse at the stop light. This is because the model assumes the car will stop at 50 seconds and continue speeding up in the opposite direction.
takando12

## Homework Statement

A driver applies brakes on seeing a traffic signal 400 m ahead. At the time of applying brakes the vehicle was moving with 15m/s and retarding with 0.3m/s2. The distance of the vehicle after 1 min from the traffic light is?
A) 25m B) 375m C) 360m D) 40m

## The Attempt at a Solution

Using v=u+at I found the time that the car takes to come v=0 is 50 sec. And using s=ut+1/2at2 I found the distance it traveled in 50 sec is 375m . Hence distance from the traffic light is 25m.
The same problem , this time using s=ut+1/2at2 and t=60 secs (this is what i did first) , i got s= 360m and distance from traffic light =40m. Why exactly is this not working? Is the reason that the equation gives me this answer is that the equation assumes that the car is going to stop at t=50 sec and then continue speeding up in the opposite direction? Please help.

takando12 said:
Is the reason that the equation gives me this answer is that the equation assumes that the car is going to stop at t=50 sec and then continue speeding up in the opposite direction? Please help.
Yes, exactly.

You are expected to model the situation of a person driving up to a stop light. (People don't reverse at stop lights).

Your model was: acceleration = -0.3 m/s/s

But the better model is: For time 0<t<T acceleration = -0.3 m/s/s; for time t>T acceleration = 0 (where T is the time to come to a stop).

takando12
Nathanael said:
Yes, exactly.

You are expected to model the situation of a person driving up to a stop light. (People don't reverse at stop lights).

Your model was: acceleration = -0.3 m/s/s

But the better model is: For time 0<t<T acceleration = -0.3 m/s/s; for time t>T acceleration = 0 (where T is the time to come to a stop).

thank you sir,

## 1. How do you define "retardation" in this context?

Retardation, in this context, refers to the slowing down or delay of traffic flow due to various factors such as congestion, accidents, or construction.

## 2. What are the possible solutions for the retardation problem?

There are several possible solutions for this problem, including implementing traffic signal optimization, increasing road capacity, improving public transportation options, and implementing intelligent transportation systems.

## 3. How can traffic signal optimization help solve the retardation problem?

Traffic signal optimization involves adjusting the timing of traffic signals to improve traffic flow and reduce delays. This can help reduce the amount of time vehicles spend waiting at red lights, thereby reducing overall traffic congestion and improving travel time.

## 4. What factors should be considered when designing a solution for the retardation problem?

When designing a solution for the retardation problem, factors such as traffic volume, peak travel times, road infrastructure, and potential budget constraints should be taken into consideration. It is important to also consider the impact on both drivers and pedestrians.

## 5. How can data analysis and technology be used to address the retardation problem?

Data analysis and technology can play a crucial role in addressing the retardation problem. By collecting and analyzing traffic data, patterns and areas of congestion can be identified, and solutions can be tailored accordingly. Intelligent transportation systems, such as real-time traffic monitoring and adaptive traffic signals, can also be implemented to help manage and optimize traffic flow.

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