PhysicsA particle starting from rest reaches a maximum velocity ‘v’ with a uniform acceleration and comes to rest with a uniform deceleration by covering a total distance ‘s’ moving along a straight line. The total time of motion is:

A particle starting from rest reaches a maximum velocity ‘v’ with a uniform acceleration and comes to rest with a uniform deceleration by covering a total distance ‘s’ moving along a straight line. The total time of motion is:

  1. A

    sv

  2. B

    2sv

  3. C

    2s3v

  4. D

    s2v

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    Solution:

    The particle starts from rest.

    u = 0

    Uniform acceleration = α
    For t = t1
    We get, 1v=αt1

    Travelled distance =x

    We get, x=12αt12    ______(1)

    Later it started retarding for t2 and come to rest

    u = αt1 , acceleration=α

    v=0 , time taken =t2

    We get v=αt1=βt2 _________(2)

    The distance travelled by it is (s−x)  where s is the total distance travelled

    s−x=12βt22    ______________(3)

    We get from (1) & (3)                         

    s=12αt12+12βt22                                 From (2) we get α=vt1, β=vt2           

    s=12vt1t12+12vt2t22

    s=12vt1+12vt2

    s=v2(t1+t2)lett=t1+t2

    2s=vtt=2sv   

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