The displacement of a particle is given by x = (t - 2)2, where x is in metre and t in second. The distance covered by the particle in first 4 seconds is

Given,                x = (t - 2)2 Velocity,           v=dxdt=ddt(t-2)2=2(t-2)ms-1Acceleration,   a=dvdt=ddt[2(t-2)]=2(1-0)=2 ms-2 When   t=0; v=-4 ms-1,t=2 s; v=0 ms-1                             t = 4s;  v = 4 ms-1v-t graph is shown in figure below.Distance travelled = Area under the v-t graph                              =∣ Area OAC∣+ Area ABD                               =4×22+12×2×4=8 m