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

Velocity of the particle $\mathrm{v}=\frac{\mathrm{dx}}{\mathrm{dt}}=2(\mathrm{t}-2)$. Hence particle changes direction at t=2 as velocity changes from negative to positive at that instant.

Therefore total distance covered by the particle from t=0 to t=4 $=\left|{\mathrm{x}}_{\mathrm{t}=2}-{\mathrm{x}}_{\mathrm{t}=0}\right|+\left|{\mathrm{x}}_{\mathrm{t}=4}-{\mathrm{x}}_{\mathrm{t}=2}\right|=4+4=8 \mathrm{m}$