A particle moves along x-axis and its acceleration at any time t is a = 2 sin ⁡ ( π t ), where t is in seconds and a is in m / s 2 . The initial velocity of particle (at time t=0) is u=0. Then the distance travelled (in meters) by the particle from time t=0 to t=t will be A) 2 π 2 sin ⁡ π t − 2 t π B) − 2 π 2 sin ⁡ π t + 2 t π C) 2 t π D)None of these

Question

A particle moves along x-axis and its acceleration at any time t is   a  =  2  sin  ⁡  (  π  t  ), where t is in seconds and a is in   m      /        s    2  . The initial velocity of particle (at time t=0) is u=0. Then the distance travelled (in meters) by the particle from time t=0 to t=t will be A)      2          π      2        sin  ⁡  π  t  −            2      t        π  B)  −      2          π      2        sin  ⁡  π  t  +            2      t        π  C)            2      t        π  D)None of these

Raymond Patel · Accepted Answer

The right answer is D   −      2          π      2        sin  ⁡  π  t  +            2      t        π    a  =  sin  ⁡  π  t  ∴  ∫  d  v  =  ∫  2  sin  ⁡  π  t  d  t  v  =  −      2    π    cos  ⁡  π  t  +  CAt t=0, v=0(  ∵ u=0)  ∴  C  =      2    π    ⇒  v  =      2    π    (  1  −  cos  ⁡  π  t  )Note: Velocity is always non-negative as   cos  ⁡  θ  ≤  1. Thus, particle always moves along positive x - direction. As velocity, v=dS/dt  ∴ Distance from time t=0 to t is  S  =      ∫          0              t            2    π    (  1  −  cos  ⁡  π  t  )  d  t  =      2    π    [  t  −      1    π    sin  ⁡  π  t      ]          0              t        =      2    π    t  −      2          π      2        sin  ⁡  π  t The particle&#039;s travel distance from time t=0 to t   s  =            2      t        π    −      2          π      2        sin  ⁡  π  t

Answered question

Answer & Explanation

New Questions in Force, Motion and Energy