Acceleration versus x and potential energy versus x graph of a particle moving along x-axis is as shown in figure. Mass of the particle is 1 kg and velocity at x = 0 is 4 m/s. Match the following at x = 8m.

`{:(,"column I","columnII",),((A),"Kinetic Energy",(P),120 J),((B),"Work done by conservative forces", (Q) 240 J,),((C),"Total work done on the particle", (R) 128 J,),((D),"Work done by forces other than conservative forces", (S) 112J,),(,,(T),"None"):}`

Answer

`A - R; B - Q; C - P ; D - S`

Explanation

`(v_f^2 - v_i^2) = 2 xx "area of a - x graph" = (v^2 - 4^2)/(2) = 120, v^2 = 16 + 240 = 256, v_(f) = 16m//"sec"`
`implies KE_(f) = 1/2 (1)(16)^(2) = 128 J , " "Delta KE = 1/2 m (v_f^2 - v_i^2) = 120 J`
Work done by all the forces , Work done by conservative forces =
`U_(i) - U_(f) = 240 J`
Work done by other forces = Total work done – Work done by conservative forces = -120 J.