Home
Class 11
PHYSICS
A man is d distance behind the bus when ...

A man is d distance behind the bus when the bus starts accelerating from rest with an acceleration `a_(0)`. With what minimum constant velocity should the man start running to catch the bus

A

`sqrt(4a_(0)d)`

B

`sqrt(3a_(0)d)`

C

`sqrt(2a_(0)d)`

D

`sqrt(a_(0)d)`

Text Solution

Verified by Experts

The correct Answer is:
C

The man catches the bus at point `P`, after time t (uniform motion):
`d+s=v t …(i)`
(accelerated motion):
`s=0+1/2a_(0)t^(2) …(ii)`
From (i) and (ii)
`d+1/2a_(0)t^(2)=vt`
`a_(0)t^(2)-2v t+2d=0`
The man will catch the bus, if time t is real, for time t to be real
`[(-2v)^(2)-4 a_(0).2d]ge0`
`v^(2)-2 a_(0)dge0`
`vgesqrt(2a_(0)d)`
`v_("min")=sqrt(2a_(0)d)`
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • MOTION IN A STRAIGHT LINE

    CP SINGH|Exercise EXERCISES|128 Videos

  • MOTION IN A PLANE

    CP SINGH|Exercise Exercises|69 Videos

  • NEET PREVIOUS YEAR

    CP SINGH|Exercise Solved Questions|64 Videos

Similar Questions

Explore conceptually related problems

A boy is moving with constant velocity v_(0) on a straight road. When he is at a distance d behind the bus, the bus starts from rest and moves with a constant acceleration alpha . Find the minimum value of v_(0) so that the boy catches the bus.

A man is 10m behind the bus stop when the bus left the stop, with an acceleration of 2m//s^(2) . What should be the minimum uniform speed of man so that he may catch the bus? If he runs with required minimum speed then how much time it will take to catch the bus?

Knowledge Check

  • A man is 45 m behind the bus when the bus starts acceleration from rest with acceleration 2.5(m)/(s^2) . With what minimum velocity should man start running to catch the bus?

    A
    12 m/s
    B
    14 m/s
    C
    15 m/s
    D
    16 m/s

  • A man is 25 m behind a bus, when bus starts accelerating at 2 ms^(-2) and man starts moving with constant velocity of 10 ms^(-1) . Time taken by him to board the bus is

    A
    2 s
    B
    3 s
    C
    4 s
    D
    5 s

  • A particle starts from rest with constant acceleration. The ratio of space-average velocity to the time average velocity is :-

    A
    `1//2`
    B
    `3//4`
    C
    `4//3`
    D
    `3//2`

    • Similar Questions

    Explore conceptually related problems

    A man 16 m behind the door of a train when it starts it starts moving with an acceleration a=2 ms^(-1) .The man runs with a msximum constant speed to get into the train. How for does he have to run and after what time does he get the train ? What is his maximum constant speed ?

    A student is standing at a distance of 50 metres from a bus. As soon as the bus begins its motion (starts moving away from student) with an acceleration of 1 ms^-2 , the student starts running towards the bus with a uniform velocity u . Assuming the motion to be along a straight road. The minimum value of u , so that the student is able to catch the bus is :

    A man is at a distance of 6 m from a bus. The bus begins to move with a constant acceleration of 3 ms^(−2) . In order to catch the bus, the minimum speed with which the man should run towards the bus is

    A particle starts from rest and moves with constant acceleration. Then velocity displacement curve is:

    A body P starts from rest with an acceleration a_(1) . After 2 seconds, another body Q starts from rest with an acceleration a_(2) from the same point. If they travel equal distances in the fifth second after starting of the motion of the P, then the ratio a_(1) : a_(2) is equal to

    Home
    Profile