Question

The driver of a train A moving at a speed of 30 ms–1 sights another trainB moving on the same track at a speed of 10 ms–1 in the same direction. He immediately applies brakes and achieves a uniform retardation of 2 ms–1. To avoid collision, what must be the minimum distance between the trains?      

Solution

Correct option is

100 m

 

The relative speed of train A with respect to train B = 30 – 10 = 20 ms–1. To avoid collision, let the minimum distance between them be s. this means that the relative speed must reduce to zero when the distance covered is s. Using  we have

        

Which gives s = 100 m.

SIMILAR QUESTIONS

Q1

A train is moving southwards at a speed of 30 ms–1. A monkey is running northwards on the roof of the train with a speed of 5ms–1. What is the velocity of the monkey as obserced by a person standing on the ground?

Q2

A jet airplane traveling from east to west at a speed of 500 kmh–1 ejects out gases of combustion at a speed of 1500 kmh–1 with respect to the jet plane. What is the velocity of the gases with respect to an observer on the ground?   

 

Q3

A police van moving on a highway with a speed of 36 km h–1 fires a bullet at a thief’s car speeding away in the same direction with a speed of 108 km h–1. If the muzzle speed of the bullet is 140 ms–1, with what speed will the bullet hit the thief’s car?    

Q4

Car A is moving with a speed of 36 km h–1 on a two-lane road. Two carsB and C, each moving with a speed of 54 km h–1 in opposite direction on the other lane are approaching car A. At a certain instant when the distance AB = distance AC = 1 km, the diver of car B decides to overtakeA before C does. What must be the minimum acceleration of car B so as to avoid an accident?   

Q5

The driver of a train A moving at a speed of 30 ms–1 sights another trainB moving on the same tack towards his train at a speed of 10 ms–1. He immediately applies brakes and achieves a uniform retardation of 4 ms–2. To avoid head-on collision, what must be the minimum distance between the trains?    

Q6

A 120 metre long train is moving west at a speed of 10 ms–1. A small bird flying east at a speed of 5 ms–1 crosses the train. What is the time taken by the bird to across the train?