# The speed of train increases at a constant rate alfa from zero to V and then remains constant for an interval and finally decreses to zero at a constant rate Beta. If L be the total distance travelled then total time taken is?

2
by paaresha
what is the time interval for which it remains constant

2014-08-10T09:56:04+05:30
(i) velocity inc. from 0 to V,
use first equation v = u + a*t : u = 0, v = V, a = α

this gives t =

use second equation s = u*t +  : u = 0, a = α, t =

this gives s1 =

(ii) velocity dec. from V to 0,
use first equation v = u + a*t : u = 0, v = V, a = -β

this gives t =

use second equation s = u*t +  : u = V, a = -β, t =

this gives s2 =

So total distance traveled d =

(iii) Thus distance traveled during constant velocity phase = L -

So time taken to travel this distance T =  ->

So total time taken to cover total distance L, =
->

2014-08-10T12:21:43+05:30

### This Is a Certified Answer

Certified answers contain reliable, trustworthy information vouched for by a hand-picked team of experts. Brainly has millions of high quality answers, all of them carefully moderated by our most trusted community members, but certified answers are the finest of the finest.
V = 0 + α t1      => t1 = V / α
S1 = 0 t + 1/2 α t1²  = 1/2 α V² / α² = 1/2 V²/α

S2 = V t2

0 = V - β t3    => t3 = V/β
S3 = (0+V)/2 * t3  = average speed * time
=  1/2 V V / β = 1/2 V² / β
Total distance L = 1/2 V² (1/α + 1/β) + V t2
t2 =  [ L/V - 1/2 V(1/α+1/β) ]

Total time taken =   V/α + L /V - 1/2 V / α - 1/2 V/β + V/β
=  V/2 (1/α + 1/β ) + L/V