Question

A particle is moving with initial velocity u and having acceleration equal to kt where K constant find out velocity after time t.​

Answer 1

Answer:

Refer to the given attachment

Answer 2

 The displacement of a particle at time t is given s = ut + 1/2at2

At time (t - 1), the displacement of a particle is given by

S' = u (t-1) + 1/2a(t-1)2

So, Displacement in the last 1 second is,

St = S - S'

= ut + 1/2 at2 – [u(t-1)+1/2 a(t-1)2 ]

= ut + 1/2at2 - ut + u - 1/2a(t - 1)2

= 1/2at2 + u - 1/2 a (t+1-2t) =  1/2at2 + u - 1/2at2 - a/2 + at

S = u + a/2(2t - 1)

So, velocity = {u+a/2(2t-1)}/t

                    = u+a /2t(2t-1)