Question

Kinetic energy of a particle (K.E) moving along x-axis depends on its position (x) and time (t) as KE = At^2/B+x^1/2 +Cx^3/2 / D+t^2 . The dimensional formula of ABC/D is

Answer 1

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)

(b) Putting the values of u = 2 m/s, a = 1 m/s2 and t = 5 sec, we get

S = 2 + 1/2(2 x 5 - 1) = 2 + 1/2 x 9

= 2 + 4.5 = 6.5 m  

(Ans): 6.5 m