Scalars, Vectors, and Descriptors of Motion -- Stop or speed up to avoid running the red light?

[paumndi]

Homework Statement:

A regular intersection is 15 meters wide, and the time it takes for a traffic light to turn from yellow to red is only 3 seconds.

June cruises down the road at a speed of 61.2 km/hr, and approaches the intersection just as the traffic light turns yellow. She is 29 meters away from the rear side of the intersection. Should she try to stop, or should she speed up to cross the intersection before the light turns red? The car’s length is 10 meters, maximum deceleration is –5 m/s2, and its maximum acceleration is 0.6 m/s2. Ignore her reaction time.

Relevant Equations:

Formula of displacement without time

 

[PeroK]

Is there more of your solution to come?

 

[paumndi]

Is there more of your solution to come?

my full solution is uploaded

 

[PeroK]

my full solution is uploaded

I thought the question was "should she stop or speed up"?

 

[paumndi]

I thought the question was "should she stop or speed up"?

yes it is

 

[PeroK]

yes it is

What's your answer?

 

[paumndi]

What's your answer?

She has enough time to stop but not cross even if she speeds up. Though I am very unsure of my answer.

 

[PeroK]

She has enough time to stop but not cross even if she speeds up. Though I am very unsure of my answer.

It looks like a silly question to me. First, the driver can't know she is going at exactly $61.2 \ km/h$. Nor, the car's braking and acceleration capability. Nor, the precise distance to the lights etc. Also, a car can't possibly be limited to an acceleration of $0.6 \ m/s$.

PS now that I've seen the full question, it is quite sensible and is more or less asking for a) and b).

What it should ask a) if she brakes, where does she stop? b) If she speeds up, where is the rear of her car when the lights change to red.

In any case, that's what I think you should calculate explicitly. Then, draw a conclusion about which course of action is better.

Your first calculation looks correct: $28.9 \ m$. Note that units are important.

Your second calculation: $t = 33$ makes no sense to me. And the units are missing.

In any case, neither is an answer to the question asked.

 

[paumndi]

This is what they taught us and I was just using this guide to answer the question.

 

[PeroK]

This is what they taught us and I was just using this guide to answer the question.

I don't have an answer to that!

 

[BvU]

How far does the young lady go if she acccelerates ?

(and what is the speed limit ?)

$\$

 

[paumndi]

How far does the young lady go if she acccelerates ?

(and what is the speed limit ?)

$\$

 

[vela]

Can you answer this subquestion? Suppose she decides to stop. Can she stop in time?

 

[paumndi]

Can you answer this subquestion? Suppose she decides to stop. Can she stop in time?

i'm sorry, all the information i have is on the image

 

[kuruman]

It looks like a silly question to me. First, the driver can't know she is going at exactly 61.2 km/h. Nor, the car's braking and acceleration capability. Nor, the precise distance to the lights etc. Also, a car can't possibly be limited to an acceleration of 0.6 m/s.

Not so silly or far fetched if you think that "June" might be an AI name like "Siri" and "Alexa". When "June" steers the car, all of the above are known to "her" including but not limited to, air speed, temperature, barometric pressure, and GPS coordinates.

 

[BvU]

i'm sorry, all the information i have is on the image

Yes, we can see it too. How far does she go/where does she end up when she decides to brake ?