Kinematics Car Distance Problem

[blumfeld0]

I have a problem that I just can't get a handle on.
You have a car that drives from A to B in 1620 seconds and then B to C.
The total distance from A to C is 10,000 meters (A to C is a straight line)
The acceleration of the car from B to C is .2 m/s^2
I need to know how long the car takes to go from B to C IF it it travel from
A to C in a total time of LESS than 1800 seconds (30 minutes)
the distance from A to B is 8900 meters and B to C is 1100 meteres

Thank you

blumfeld0

 

[tony873004]

IF it it travels from

A to C in a total time of LESS than 1800 seconds (30 minutes)

&

The total distance from A to C is 10,000 meters (A to C is a straight line)

This is like saying the car drives from A to C doing at least 20 km/hr

So your question becomes:
How long does it take a car to travel 1100 meters given that its initial velocity is at least 20 km/hr and it is accelerating at 0.2 m/s^2?

I'd still need to know what initial velocity is. Without that, I could only give you a range of answers, using 20 and infinity as velocity to compute the answer.

Maybe your answer is supposed to be in the form:
"The car will take no longer than ____ to travel from B to C."

 

[sebas531]

well, I might be wrong but i would say it would take about 50.74 seconds. First, i found the velocity of the car from a to b (v=d/t), knowing that i had the initial velocity to start thinking about the problem from point b to c. Then i use the formula vf^2=vi^2+2ad for and I plugged in for vi= 5.49 m/s a=.2m/s^2 (given) d= 1100m (from point b to c) then i would have the final velocity with that i used v=d/t and changed it to t=d/v and i got 50.74 seconds. I might be wrong and if you find the right answer let me know

 

[tony873004]

I think you got it wrong. Disregard my original post. I fell for the irrelevant data trick.

Once you find your final velocity, compute your average velocity (B to C) and use that in your t=d/v formula.

Or use the formula xf=xi+vit+0.5at^2 and use the quadratic equation. I get the same answer both ways.

 

[sebas531]

It is ok (in a way) if I got it wrong. It is all about knowing how to do it. However, what irrelevant data are you talking about?... I got vf=21.68, i know that you said that after you plugged the final velocity into both of the formulas you got the same answer, however, i did not, so yes, i see that i could have made a mistake. It would be helpful if you would tell me perhaps how you achieved your answer and ofcourse state all of the calculations you made, that way i could compare, understand, and learn how to do the problem. Thank you.

 

[tony873004]

What answers did you get?

The irrelevant data is this: "it travel from A to C in a total time of LESS than 1800 seconds".

I didn't use 1800 for anything.

No, I didn't plug the final velocity into either formula. The 1st formula (t=d/v) wants average velocity for v, and the 2nd formula wants initial velocity.
Average velocity = (final velocity + initial velocity) / 2

Did you try the quadratic way?

 

[sebas531]

Everytime i use a different formula i get a different answer which has confused me in a way, quadratic way? if by that you mean "xf=xi+vit+0.5at^2" what is x? distance? if it is then i have never seen such equation before and it gives me a negative distance which i cannot take the sq root of since it would be a non real answer. For such reason, i don't believe that x would stand for distance. After using some other formulas i have gotten 81 seconds using avg velocity. I do not understand why you did not use avg velocity.

 

[tony873004]

I got 81 too.

I can't seem to get TEX to work in preview mode, so this will be ugle

The quadratic way: (this way is harder, but it's good to know how)

xf=xi+vit+0.5at^2

1100=0+5.49t+0.5*0.2t^2

set it equal to 0

0.1t^2+5.49t-1100=0

a=0.1
b=5.49
c=-1100

t=(-b+-sqrt(b^2-4ac))/2a

Since it's + or - sqrt, you need to do it twice and discard the unreasonable answer:

t=(-5.49+sqr(5.49^2-4*0.1*-1100))/(2*0.1)

t=80.96 (accept this answer since it agrees with your other answer and it seems reasonable)

or

t=(-5.49-sqr(5.49^2-4*0.1*-1100))/(2*0.1)
t=-135.9 (disragerd this answer since your time can't be negative)

 

[sebas531]

Thank you very much, tony873004, for i have learned some things thanks to you. Things that i had not learned or perhaps that i had not paid enough attention to, which i regret.