A particle A of mass 10/7 kg is moving in the positive direction of x-axis. At initial position x = 0, its velocity is 1 ms-1, then its velocity at x = 10 m is (use the graph given)

Area under P-x graph    =∫pdx=mdvdtvdx=∫1v mv2dV=mv331v=107×3v3−1From the graph, area =12(2+4)×10=30107×3v3−1=30v=4ms−1Alternative method:From graph P=0.2x+2mvdvdxv=0.2x+2mv2dv=(0.2x+2)dxNow integrating both sides, we get∫1v mv2dv=∫010 (0.2x+2)dxv=4ms−1