Kinematics Problem: Get Help Solving

[HP-Physics]

Homework Statement

Calculate the distance that the driver has traveled in the process.

Relevant Equations

A group of n people needs to move from point A to point B about a distance AB=l apart, but they only have a bike and only one of them is capable of motorcycling (called the driver). The bike has only 2 seats. For everyone to depart from A and arrive in B at the same time, they decide to let the first man accompany the driver (while the others were walking) to the point T_1 and get the first man off. Then, the driver immediately turns back to the point D_2 to come along with the second man to chase the first man and they meet at the point T_2. Then, the second man walks together with the first one to B and the driver comes back to the third one. The process continues to the k man, he would be picked up at T_k and gotten off at D_k to meet the others. Know that n>2, the velocity of all walkers is the same and equal to u. The velocity of the motorbike is v with one person and with two people, it is v^'.

I'm not sure about my answer

 

[lewando]

You need to provide an attempt at a solution before you can get any help, per rules. Why are you not sure about your answer? How did you arrive at your answer?

 

[HP-Physics]

My total distance is this equation

 

[lewando]

Do you want us to check it for you? We do that, on occaision, depending on what else is goin' on in our lives. You did not respond to my two questions. Please do.

 

[HP-Physics]

Do you want us to check it for you? We do that, on occaision, depending on what else is goin on in our lives. You did not respond to my two questions. Please do.

Yep, please check it for me. I think it's a difficult one and want to share for everyone. Just that :)

 

[haruspex]

My total distance is this equation

That doesn't look right to me at all. I would expect to see n as an exponent in the answer.
It is certainly wrong at n=2, but that can be corrected merely by changing one sign in your answer.

Edit: all nonsense... see post #9.

Please post your working.

 

[HP-Physics]

That doesn't look right to me at all. I would expect to see n as an exponent in the answer.
It is certainly wrong at n=2, but that can be corrected merely by changing one sign in your answer.

Please post your working.

Yes, with n=2 it's quite simple and the original of this exercise. I'm trying to do with n>2. Okie

 

[HP-Physics]

I'm really sorry about my English grammar, it is not good

 

[haruspex]

I'm really sorry about my English grammar, it is not good

I take it all back.
My intuition about the form of the answer was based on a wrong view of the question, and I blundered in checking your answer at n=2.
I get the same answer as you do, by a somewhat different route.

 

[HP-Physics]

I take it all back.
My intuition about the form of the answer was based on a wrong view of the question, and I blundered in checking your answer at n=2.
I get the same answer as you do, by a somewhat different route.

How do you think, about this problem?

 

[haruspex]

How do you think, about this problem?

Do you mean, how did I approach it?

 

[HP-Physics]

Not really, I mean if you have any better solutions

 

[haruspex]

Not really, I mean if you have any better solutions

Don't know that it is better, still quite messy.
I used y for forward motoring step distance, y-x for reverse motoring step, t for time of one of each.
t = y/v'+(y-x)/v = x/u
L = y + (n-2)x
From which we can find x and y.
Total distance = y + (n-2)(2y-x)