Stuck in a question from exam -- Car decelerating to avoid hitting an obstacle

[shuumi]

Homework Statement

it's about the cinematics (mru, mrua, mcu and free fall...?)

Relevant Equations

A car going 120 km / h when the driver sees an obstacle to 90 meters away, step on the brake and the car applies to deceleration of 6 m / s ?, if the reaction time of the driver is 0.15 seconds to figure out whether it will stop before reaching the obstacle or collide with him. (using the formulas of cinematics, movements)

i tried but i wasn't able, maybe i choose the wrong formulas in the wrong time.

 

[kuruman]

Hi @shuumi and welcome to PF.

According to our rules you must show some effort towards the solution before you can receive help. Show us what you tried and what your thoughts were.

 

[shuumi]

Hi @shuumi and welcome to PF.

According to our rules you must show some effort towards the solution before you can receive help. Show us what you tried and what your thoughts were.

Okay, i will tell you the problem, i had the exam, i got literally a 4,5/10, many exercises similar to this are all false, including this one, i don't have the exam with me, the teacher said that she will do a recuperation to the most of the class with similar questions, so i need to know how to answer it correctly, including an explanation if it's possible to understand it.

 

[shuumi]

i only took a picture of it in class, you can see that i may start with the wrong formula... but i didn't took a whole picture (It's in spanish btw since I'm from there)

 

[kuruman]

Before trying to find a formula that will give you the answer, you need to have a strategy. What is your strategy here? It looks like you tried to calculate the time it will for the car to travel the 90 m to the obstacle under constant deceleration. That doesn't help much, unless you have a strategy in place that tells you what to do with it once you have it.

Also, you did not take into account the reaction time of 0.15 s. How does that figure into the picture? Think about all this and come up with a strategy, no equations - no numbers, just words. Start with "I will first find $\dots~$"

Furthermore, please be considerate to those who are trying to help you and post your pictures in their proper orientation.

 

[shuumi]

Before trying to find a formula that will give you the answer, you need to have a strategy. What is your strategy here? It looks like you tried to calculate the time it will for the car to travel the 90 m to the obstacle under constant deceleration. That doesn't help much, unless you have a strategy in place that tells you what to do with it once you have it.

Also, you did not take into account the reaction time of 0.15 s. How does that figure into the picture? Think about all this and come up with a strategy, no equations - no numbers, just words. Start with "I will first find $\dots~$"

yes i agree with you i tried to do a figure or a drawing to understand the situation since i always use it but i didn't know what to do, the way you said: "unless you have a strategy in place that tells you what to do with it once you have it", that literally what happened to me, when i calculated this, i was like and what next? I got confused, and i started with a new formula that it isn't showen which was wrong too.

 

[shuumi]

For the 0'15 seconds, i though that after calculating the time, i have to like add it or something, but somehow it looked wrong to me, i started with the wrong formula, and i wasn't even sure about what i was doing exactly.

 

[kuruman]

If you want to learn how to do problems like this, you need to learn to construct a strategy before you look around for formulas to apply. Can you make a plot of the velocity of the car as a function of time? Start at time t = 0 which is the moment the driver sees the obstacle. What does this plot look like? Please post your best effort and make sure it's right side up. Do that and we will see where to go from there.

 

[Delta2]

I think @kuruman can guide you well in this so my presence is redundant. All I wanted to say is that:

The physics branch that deals with problems like the one here is called Kinematics , not cinematics (I know "c" is usually pronounced as "k" when it is the starting letter, but looking at cinematics one would thought it has something to do with cinema.

 

[shuumi]

man i really apologize but you're not dealing with a very good student, I'm trying to put all my efforts in this revision for the exam, look, as you said, we don't need to forget the 0'5 seconds..okay, i trying to do it, but the distance is so low and small, now I'm lost again, the idea of making a strategy is the best one, but I'm not really good at this.

 

[shuumi]

I think @kuruman can guide you well in this so my presence is redundant. All I wanted to say is that:

The physics branch that deals with problems like the one here is called Kinematics , not cinematics (I know "c" is usually pronounced as "k" when it is the starting letter, but looking at cinematics one would thought it has something to do with cinema.

Oh thanks for correcting! in Spanish we say cinemática, So i though it's was the same in English but not including the a in the end of the word.

 

[kuruman]

Do you understand what a plot of velocity as a function of time looks like? It's a graph with velocity on the y-axis and time on the x-axis. It is not a bunch of equations. Can you make such a graph?

 

[shuumi]

Do you understand what a plot of velocity as a function of time looks like? It's a graph with velocity on the y-axis and time on the x-axis. It is not a bunch of equations. Can you make such a graph?

I'm not sure if I'm able to, we never use it in class, only the graphic of a horizontal and lineal line as it is showen on the photo that I've send you just now, so i don't think i can do it.

 

[PeroK]

Do you understand what a plot of velocity as a function of time looks like? It's a graph with velocity on the y-axis and time on the x-axis. It is not a bunch of equations. Can you make such a graph?

I suggest the first thing to sort out is the initial velocity. It's given as $120 \ km/h$, but that needs to be converted to SI units ($m \ s$).

 

[erobz]

The driver doesn't start accelerating until after he is able to react. First, how far will they travel in that amount of time? Remember to convert to consistent units ( preferably meters ).

 

[jbriggs444]

There are a couple of generic strategies that work for many problems.

1. Play the scenario forward.

What is the situation now? How will will it evolve over time. Will there be a change in conditions or an end to the scenario? When will that be? What will the situation be then? Play that scenario forward. Repeat until you get to the finishing situation.

2. Tree search. (Top-down, bottom-up, meet-in-the-middle)

Make a list of what you know. See what you could calculate from what you do know to what you can know.

Identify what you need to know. See what things that, if you knew them, would allow you to calculate what you need to know. This what you want to know.

You can iterate up from the bottom figuring out what else you want to know that would help you out. Or down from the top seeing what else you could calculate based on what you can know. You can do all this without actually calculating -- just figuring out what you could calculate.

Once you meet in the middle, you can do the calculations.

For this problem, since the initial conditions are all known, my inclination is to go with "Play it forward". This will end up looking a lot like the top-down tree search.

 

[kuruman]

I suggest the first thing to sort out is the initial velocity. It's given as $120 \ km/h$, but that needs to be converted to SI units ($m \ s$).

OP has already done that. It's the first thing he did in the posted solution in #4.
To @shuumi: Suppose the obstacle is by the side of the road and there is no possibility that the car will hit it. Nevertheless, the driver applies the brakes as described. Can you find the distance the car will travel before it stops? That should tell you something.

 

[haruspex]

View attachment 301656man i really apologize but you're not dealing with a very good student, I'm trying to put all my efforts in this revision for the exam, look, as you said, we don't need to forget the 0'5 seconds..okay, i trying to do it, but the distance is so low and small, now I'm lost again, the idea of making a strategy is the best one, but I'm not really good at this.

For constant acceleration, there are five "SUVAT" equations. There are slightly different versions taught, but it gets its name from the five variables used in the basic system:
s = displacement
u = initial velocity
v = final velocity
a = acceleration
t = time
Corresponding to these there are five equations, each omitting one of the five variables. So given any three of the above you can find the other two.

Faced with a problem, these are the steps:
1. Is the acceleration constant throughout? If not, can we break it into stages so that the acceleration is constant in each? What variables connect the stages?
2. In a given constant acceleration stage, which four variables do we care about? Those are the variables which are known, or which we need to find, or which connect stages. Select the SUVAT equation that involves those four.
3. Count your unknowns and equations. If you have more unknowns than equations look around for some info you have not used. If more equations than unknowns, one of the equations is redundant and should be thrown away to avoid going down a blind alley. If equal numbers, solve!

You have probably already memorised the five equations. Practise applying the above procedure to several problems.

 

[shuumi]

OP has already done that. It's the first thing he did in the posted solution in #4.
To @shuumi: Suppose the obstacle is by the side of the road and there is no possibility that the car will hit it. Nevertheless, the driver applies the brakes as described. Can you find the distance the car will travel before it stops? That should tell you something.

Okay so, the first thing that i did in this picture i think it's correct, the second one maybe wrong, if we suppose that the Xo = 0'75 m / Vo = 120km/h = 33'3 m/s / a = -6m/s² (since the velocity is not augmented). so we need to search for two things: the time and the final distance. please correct me if I'm wrong.

 

[erobz]

View attachment 301657
Okay so, the first thing that i did in this picture i think it's correct, the second one maybe wrong, if we suppose that the Xo = 0'75 m / Vo = 120km/h = 33'3 m/s / a = -6m/s² (since the velocity is not augmented). so we need to search for two things: the time and the final distance. please correct me if I'm wrong.

The first thing you did does not look correct. Ask yourself: "before the driver can react, can they accelerate?"

 

[shuumi]

The first thing you did does not look correct. Ask yourself, before the driver can react, can they accelerate?

oh my God no, the driver can't. But if it isn't this formula, then am i going to use the normal formula of V = d/t ??

 

[haruspex]

the first thing that i did in this picture i think it's correct,

Really?
You have plugged in $v_0=0, a=6m/s^2, t=0.15s$. 0.15s is the driver's reaction time. What does that mean? What is happening during that time?

How you calculated 0.15 x 6 = 3 is also a cause for concern.

 

[shuumi]

Really?
You have plugged in $v_0=0, a=6m/s^2, t=0.15s$. 0.15s is the driver's reaction time. What does that mean? What is happening during that time?

yeah you're totally right, Vo = 33,3 m/s

 

[haruspex]

yeah you're totally right, Vo = 33,3 m/s

And what is a during that time?

 

[shuumi]

And what is a during that time?

a = 0 ??

 

[haruspex]

a = 0 ??

Right. So what is $v_f$ after the 0.15s?

 

[shuumi]

Right. So what is $v_f$ after the 0.15s?

Hmm I'm not sure, 33,3 m/s ?

 

[Delta2]

Ok I said I will not post further but can't resist. I ll give you two big hints that are essentially a kind of high level strategy that @kuruman talked about. Let's see if you can fill the in between details:

1) For the first 0.15seconds the car does motion (because the driver hasnt yet pressed the break pedal) with constant speed $v_0=120km/h$. So calculate the distance $X_1$ that the car travels in the first 0.15seconds

2) After that the car does motion with constant acceleration (or we should say deceleration to be 100% accurate), it is kind of like motion in free fall only that it is horizontal and the deceleration is not g=-10m/s^2 but it is a=-6m/s^2. Calculate the distance $X_2$ that the car travels till it stops. The starting velocity here is still $v_0=120km/h$ and you should take as final velocity $v_f=0$ (that is when the car stops).

3) IF $X_1+X_2\geq 90m$ then the car collides with the obstacle. if $X_1+X_2<90m$ then the car doesn't collide.

 

[shuumi]

Really?
You have plugged in $v_0=0, a=6m/s^2, t=0.15s$. 0.15s is the driver's reaction time. What does that mean? What is happening during that time?

How you calculated 0.15 x 6 = 3 is also a cause for concern.

my bad man, my calculator is in a bad case, I've just changed it, ignore it please.

 

[shuumi]

Ok I said I will not post further but can't resist. I ll give you two big hints that are essentially a kind of high level strategy that @kuruman talked about. Let's see if you can fill the in between details:

1) For the first 0.15seconds the car does motion (because the driver hasnt yet pressed the break pedal) with constant speed $v_0=120km/h$. So calculate the distance $X_1$ that the car travels in the first 0.15seconds

2) After that the car does motion with constant acceleration (or we should say deceleration to be 100% accurate), it is kind of like motion in free fall only that it is horizontal and the deceleration is not g=-10m/s^2 but it is a=-6m/s^2. Calculate the distance $X_2$ that the car travels till it stops. The starting velocity here is still $v_0=120km/h$ and you should take as final velocity $v_f=0$ (that is when the car stops).

3) IF $X_1+X_2\geq 90m$ then the car collides with the obstacle. if $X_1+X_2<90m$ then the car doesn't collide.

Okay, after you told me all what i need to do I'm still not even sure if i did it correctly, is it correct ?? please correct me if I'm wrong.

 

[PeroK]

View attachment 301663
Okay, after you told me all what i need to do I'm still not even sure if i did it correctly, is it correct ?? please correct me if I'm wrong.

That initial distance of $5m$ seems to have been included three times! Twice would be too many, but three times is excessive, I would say!

I think your calculation for $X_2$ is correct. And, given that $X_2 > 90m$ you needn't have worried about the reaction time. Although, you added $5m$ to it.

 

[Delta2]

You did it almost correct, only mistake is that you "double count" the distance d=5m that the car travels during the 0.15second.

 

[PeroK]

You did it almost correct, only mistake is that you "double count" the distance d=5m that the car travels during the 0.15second.

Treble count, even!

 

[Delta2]

Er no its double lol, He counts it once in step 2 (where he shouldnt) and once in step 3 (where he should).

 

[shuumi]

That initial distance of $5m$ seems to have been included three times! Twice would be too many, but three times is excessive, I would say!

I think your calculation for $X_2$ is correct. And, given that $X_2 > 90m$ you needn't have worried about the reaction time. Although, you added $5m$ to it.

the second part is correct, I'm confused about the 5m thing, what is wrong about it? since the acceleration is not included, the only way to do it is by using the basic method that we know: V = d/t, do i have to use an another method? Or i have choose the wrong numbers ?