Let the resistance f = kv. So k = 0.2. Because dw=fdx. V=(dx/dt)=8t because x = 4t 2. Dx=8tdt. When x=0, t=0 to x=2t= root 2/2. So dw = 0.2 * 8t * 8t * dt =12.8t2dt, and the upper limit of the integral on both sides is 0 and the lower limit is 2/2 of the root. So W=? You can solve it yourself.