A time dependent force F=6t acts on a particle of mass 1kg. If the particle starts from rest, the work done by the force during the first 1 sec. will be :

Work done by time dependent force -W= ∫F⋅v dt- whereinWhere F and v are force and velocity vector at any instantForce is given F = 6tF = ma = mdv/dt= 6tdv/dt=6t(Since m = 1 kg)dv = 6t dtOn integrating ∫_0^vdV =6∫_0^1t dt = 3Therefore v = 3 m/sTherefore change in kinetic energy in one second = 1/2×m ×3^2-0=4.5 JHence,option(D)is correct answer.