A train is moving at a constant speed V. When | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(D) Let the speed of the first train be $V$ and the second train be $u$. Since they are moving in the same direction,the relative velocity of the firs

Vedclass · Accepted Answer

$(V - u)^2 / 2x$

Vedclass · Answer

(D) Let the speed of the first train be $V$ and the second train be $u$. Since they are moving in the same direction,the relative velocity of the first train with respect to the second train is $V_{rel} = V - u$.To avoid a collision,the first train must come to a relative rest with respect to the second train just as it reaches the distance $x$.Using the third equation of motion for relative motion: $v^2 - u_{rel}^2 = 2ax$.Here,the final relative velocity $v = 0$,the initial relative velocity $u_{rel} = (V - u)$,and the displacement is $x$.Substituting these values: $0^2 - (V - u)^2 = 2ax$.$- (V - u)^2 = 2ax$.$a = -\frac{(V - u)^2}{2x}$.The negative sign indicates retardation. Therefore,the minimum retardation required is $\frac{(V - u)^2}{2x}$.

$A$ train is moving at a constant speed $V$. When its driver observes another train in front of him on the same track and moving in the same direction with constant speed $u$. If the distance between the trains is $x$,what should be the minimum retardation of the train to avoid a collision?

Similar Questions

Explain the concept of relative displacement and its various cases.

$A$ man is $45 \, m$ behind the bus when the bus starts accelerating from rest with an acceleration of $2.5 \, m/s^2$. With what minimum velocity should the man start running to catch the bus?

Two cars $A$ and $B$ are moving in the same direction with velocities $30 \, m/s$ and $20 \, m/s$. When car $A$ is at a distance $d$ behind car $B$,the driver of car $A$ applies brakes,producing a uniform retardation of $2 \, m/s^2$. There will be no collision when ......... $m$.

Two cars are travelling towards each other at a speed of $20 \,m \,s^{-1}$ each. When the cars are $300 \,m$ apart, both the drivers apply brakes and the cars retard at the rate of $2 \,m \,s^{-2}$. The distance between them when they come to rest is: (in $\,m$)

An express train is moving with a velocity $v_1$. Its driver finds another train moving on the same track in the same direction with velocity $v_2$. To escape a collision,the driver applies a retardation $a$ to the train. The minimum time to escape a collision will be:

Vedclass Test Series

Exam Paper Generator

Online Exam Module