Linear motion, motorcyclist braking time

[rbh]

Homework Statement

Motorcyclist is driving straight, horizontal road and then he starts to brake, within 2 seconds he travelled half the braking distance. Calculate how much time it took him to travell full braking distance.

Relevant Equations

d = (Vf^2 - Vi^2) / 2a
Vf = Vi + at

I tried using equations listed above to get the answer, but I get stuck with a and Vi. What am I doing wrong?

The answer is 6.7 seconds.

 

[haruspex]

Homework Statement:: Motorcyclist is driving straight, horizontal road and then he starts to brake, within 2 seconds he traveled half the braking distance. Calculate how much time it took him to travell full braking distance.
Relevant Equations:: d = (Vf^2 - Vi^2) / 2a
Vf = Vi + at

I tried using equations listed above to get the answer, but I get stuck with a and Vi. What am I doing wrong?

The answer is 6.7 seconds.

There are five standard SUVAT equations, each involving four of the five variables s, u, v, a, t. Given any three you can find the correct other two.
The trick is to identify which are know, which are to be found, and which you don't care about.
In this question it's a bit more complicated because you have two scenarios, first 2 seconds and whole of stopping process, connected by relationships between the variables involved, e.g. same acceleration.
Write an equation or two for each scenario and see where you get to. Post what you get.

 

[Lnewqban]

Homework Statement:: Motorcyclist is driving straight, horizontal road and then he starts to brake...

Welcome, rbh!

 

[rbh]

There are five standard SUVAT equations, each involving four of the five variables s, u, v, a, t. Given any three you can find the correct other two.
The trick is to identify which are know, which are to be found, and which you don't care about.
In this question it's a bit more complicated because you have two scenarios, first 2 seconds and whole of stopping process, connected by relationships between the variables involved, e.g. same acceleration.
Write an equation or two for each scenario and see where you get to. Post what you get.

Well I got t = 4 / (0.5 - 0.5*a*t1) and -a = (4/t/2/t1), but either one of those equations are wrong or both of them.

 

[haruspex]

Well I got t = 4 / (0.5 - 0.5*a*t1) and -a = (4/t/2/t1), but either one of those equations are wrong or both of them.

You'll need to define t and t1 and explain how you get those equations. I don't know what you mean by 4/t/2/t1.

 

[PeroK]

Homework Statement:: Motorcyclist is driving straight, horizontal road and then he starts to brake, within 2 seconds he traveled half the braking distance. Calculate how much time it took him to travell full braking distance.
Relevant Equations:: d = (Vf^2 - Vi^2) / 2a
Vf = Vi + at

I tried using equations listed above to get the answer, but I get stuck with a and Vi. What am I doing wrong?

The answer is 6.7 seconds.

I get ##6.83## seconds. Tricky question!

 

[Lnewqban]

I get ##6.83## seconds. Tricky question!

By making a V versus t graph, I got the same answer, which seems to be independent from deceleration rate or initial velocity.

 

[haruspex]

I get ##6.83## seconds. Tricky question!

It's very easy if you work backwards from the stopping point. Should get 4+2√2.

 

[rbh]

Nvm those equations I wrote are wrong. I still don't understand what should I do. Should I work with the graph? If yes what do I need to find first? Accelaration before he started braking?

 

[PeroK]

Nvm those equations I wrote are wrong. I still don't understand what should I do. Should I work with the graph? If yes what do I need to find first? Accelaration before he started braking?

You have three options:

1) Work through the SUVAT equations and try to find the total stopping time ##t## in terms of ##t_1##, the time to travel half the total distance.

The risk is that you go round in circles and never seem to be able to get rid of ##u, a, d##, the initial speed, deceleration and stopping distance.

2) Use the fact that distance is the area under a speed vs time graph to turn this into a geometry problem. See post #7.

3) This problems suggests that there is a general relationship between ##t## and ##t_1## for any choice of ##u, a, d##. In particular, you might expect ##t = kt_1## for some cosntant ##k## that is independent of ##u, a, d##. So, pick some numbers, do a specific problem and see what you get for ##k##. Then apply that with ##t_1 = 2s##.

 

[haruspex]

Nvm those equations I wrote are wrong. I still don't understand what should I do. Should I work with the graph? If yes what do I need to find first? Accelaration before he started braking?

One problem with solving it graphically is that you will have to assume that the actual acceleration etc. do not matter. Working algebraically you will find out whether they do.
It is hard to help you with the algebra if you won't post all your working.
As I mentioned in post #2, there are five SUVAT equations to choose from, and as I indicated in post #8, the easiest way is to use the one that does not involve the initial velocity.
Can you write that equation? It's the same as the one that omits final velocity but with the opposite sign on the acceleration.

 

[rbh]

One problem with solving it graphically is that you will have to assume that the actual acceleration etc. do not matter. Working algebraically you will find out whether they do.
It is hard to help you with the algebra if you won't post all your working.
As I mentioned in post #2, there are five SUVAT equations to choose from, and as I indicated in post #8, the easiest way is to use the one that does not involve the initial velocity.
Can you write that equation? It's the same as the one that omits final velocity but with the opposite sign on the acceleration.

So do I use these equations?

 

[PeroK]

So do I use these equations?

They don't look very promising to me. They look complicated and it's not clear how you are going to get rid of all those unknowns.

What about my suggestion of trying with some numbers to see what happens? If you can't solve a general problem, try a specific problem with some numbers. In my opinion that's never a bad idea.

 

[PeroK]

So do I use these equations?

Since you've been on this for a few days ...

First, for a problem like this you must get all the variables and notation sorted. I suggest:

##u## is the initial speed of the motorbike

##a## is the (positive) deceleration. That means acceleration ##= -a##.

##t_1## is the time to go half the stopping distance. ##t_1 = 2s## is the only data we have.

##v## is the speed at time ##t_1##

##d## is the total stopping distance.

Where do we start? First, we know that ##u^2 = 2ad##. We also know that ##u^2 - v^2 = 2a(\frac d 2) = ad##. And that means that ##v^2 = ad##.

Does that help?