Question

a particle having initial velocity u is moving with constant acceleration for time t.find the displacement of particle in the last one second

Answer 1

V =u+at is your answer

Answer 2

Thanks for your question !

         The displacement of a particle in time (t) is given,
 s = ut + 1/2at²
        Let the time is t - 1, the displacement of a particle is :
 S' = u (t-1) + 1/2a (t-1)² - - - (Substituting t-1 as t)
     Now, we have secured S and S' value for substituting in equations. Let the equation is to be displacement of particle in one second.
The displacement of particle in last one second is : St = S - S'
                      = ut+1/2 at²-[u(t-1)+1/2 a(t-1)²]
                     = ut + 1/2at² - ut + u - 1/2 a(t-1)²
                     = 1/2at² + u - 1/2 a (t +1-2t)
                     =  1/2at² + u - 1/2at² - a/2 + at
Hence, the displacement of particle in one second will be S = u + a/2(2t-1)