Question

The greatest acceleration ordeceleration that a train may have is a.find minimum time in which the train may reach from one station to other separated by a distance d

Answer 1

So what you want to do obviously is accelerate to the midpoint and decelerate from the mid-point to the end.

Given that, how long does it take to reach the mid-point?

Answer 2

?

Answer 3

How far is the mid point from the first station? d/2.

How far does the train travel if it starts at rest and accelerates at a constant rate of a?

Answer 4

c'mon Aravind. How far does a body move if it starts at rest and accelerates at a constant rate of a for a time of t?

Answer 5

If you're not going to stay and engage with me I don't know why I bother to try and help you. This isn't the first time you walk away mid-conversation and it gets pretty boring for me if you're not going to make an effort. Sorry.

Answer 6

srry james i will try not to repeat it

Answer 7

ok. So where did you get with this question?

Answer 8

Aravind, talk to me here, not in other people's questions.

Answer 9

k

Answer 10

Have you finished this question? Where are you with it?

Answer 11

i am doing another currently

Answer 12

i am discussing with turing can u also cm

Answer 13

http://www.twiddla.com/712316

Answer 14

well, I'd like to see you finish one question (with my help) before I engage with you on another. I'm unhappy that I've never seen you reach the end of a problem.

When you're ready, let's finish this problem. Then I will help you with a new problem. But for now I'm not interested in helping you with a new one.

When you're ready, let me know here.

Answer 15

K

Answer 16

for minimum time acceleration is a

Answer 17

james?

Answer 18

Oh, ok, you want to do this now. So the train accelerates to the half way point d/2, then decelerates.

Answer 19

The first question is, how long does it take to reach d/2 if it starts from rest.

So if it accelerates at a constant rate, then velocity v at time t is
v = at.

What then is the displacement at time t?

Answer 20

If s(t) is the displacement, we want to know the time t such that
s(t) = d/2.

Hence we need a formula for s(t). What is that formula, given that v(t) = at ?

Answer 21

And you're not here? Where are you?

Answer 22

For the record
\[ s(t) = s(0) + \int_0^t v(u) \ du \]
\[ = s(0) + \int_0^t au \ du \]
\[ = s(0) + \frac{1}{2} at^2 \]
As s(0) = 0, hence
\[ s(t) = \frac{1}{2}at^2 \]

Answer 23

ya

Answer 24

so 1/2 at^2 is the answer??

Answer 25

s(t) = 1/2 . at^2. So how long does it take the train to reach the mid-point d/2 ?

Answer 26

at^2

Answer 27

No. At the mid-point
s(t) = d/2,
as s(t) is the expression for displacement at time t.

So the question is: for what value of t is this the case?