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Mechanics

Blazing goIITian

Joined:	31 Jan 2007
Post:	1069

20 Sep 2007 23:57:12 IST

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264

find time

None

A motor of an electric train can give it an acceleration of 1m/s^2 and brakes can give a retardation of 3m/s2 the shortest time in which a train can make a trip between 2 station of distance 1215 m is

Ans 56.9 sec

please give me a detailed simplified solution

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ramyani chakrabarty

Blazing goIITian

Joined: 22 Apr 2007

Posts: 2537

21 Sep 2007 01:32:05 IST

Like 3 people liked this

Yes.
Let the train starts with an accln "a " from one station ( starting from rest ) and goes for some time t₁ . Then maxm vel v = a t₁ .

Let after t₁ , the brake is applied and the train retards at rate " b " for rest ( t-t₁ ) time and finally comes to rest . { t = total time }

Then 0 = v - b ( t-t₁ ) = a t₁ - b ( t-t₁ )

or t₁ = bt / ( a + b )

So, maxm vel v = abt / ( a + b )

Now draw a v vs t graph.

Remember distance travelled = area under v-t graph

                                           = ( 1 / 2) ( maxm vel ) ( total time )

                                          = ( 1 / 2) [ abt / ( a + b ) ] t

                                         = ( 1 / 2) [ abt² / ( a + b ) ]

In this prob a = 1m /s² and b = 3 m /s²

          distance travelled = 1215 m

         So total time t = 56.9 s which is the shortest time.

p.s I can't draw. Sorry.

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