Question

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?   

Solution

Correct option is

1 ms–2

 

Let us suppose that cars A and B are moving in the positive x-direction. Then car C is moving in the negative x-direction. Therefore, 

. The relative velocityB with respect to A is . The relative velocity of C with respect to A is . At time t = 0, the distance between A and C = 1 km = 1000 m. The car C will cover a distance AC = 1000 m and just reach car A at a time t given by

            

               

                = 40 s

Car B will overtake car A just before car C does and avoid an accident, if it acquires a minimum acceleration a such that it covers a distance s = AB= 1000 m in time t = 40 s, travelling at a relative speed. Putting these values in relation     

                         

.

Which gives a = 1 ms–2

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

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?      

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?