0

Guest

Courses New

Two trains initially separated byba distance d. One train moves with velocity v1 and the othet with velocity v2,such that v1>v2.Now the train moving with velocity v1 applies a constant retardation `a`. Prove that the hap between the two trains should be d>{(v1-v2)^2}÷2a so that the trsins do not collide.

Two trains initially separated byba distance d. One train moves with velocity v1 and the othet with velocity v2,such that v1>v2.Now the train moving with velocity v1 applies a constant retardation `a`. Prove that the hap between the two trains should be d>{(v1-v2)^2}÷2a so that the trsins do not collide.

Grade:11

1 Answers

Vikas TU
14149 Points
7 years ago
For first train let the speed be v1 then after a constant accleration the eqn. of motion becomes,
(x+d) = v1*t + 0.5at^2...................(1)
For second train the eqn. would be,
x = v2*t.........(2)
solving both eqns. we get,
t = [(v1-v2) + root( -(v1-v2)^2 + 2ad)]/a
Now the roots term should be greater than eqial to zero according to its domain,
Hence,
2ad – (v1-v2)^2 greater than equal to zero.
solving we get,
d greater than (v1-v2)^2/2a
Hence Proved.

Think You Can Provide A Better Answer ?

Other Related Questions on Mechanics

View all Questions »

ASK QUESTION

Get your questions answered by the expert for free

Answer and earn gift vouchers

Win Gift vouchers upto Rs 500/-

View courses by askIITians

Design classes One-on-One in your own way with Top IITians/Medical Professionals

Click Here Know More

Complete Self Study Package designed by Industry Leading Experts

Click Here Know More

Live 1-1 coding classes to unleash the Creator in your Child

Click Here Know More

a Complete All-in-One Study package Fully Loaded inside a Tablet!

Click Here Know More