The displacement of a particle is given by x = (t – 2)² where x is in metres and t in seconds. The distance (in m) covered by the particle in first 4 seconds is$\_\_\_\_\_\_$

The distance travelled is given by x = (t−2)² = t² – 4t + 4

As velocity is given by  v = dx/dt

v = 2t − 4

Distance covered = ∫∣v∣dt

= ∣t² – 4t∣

= (4t−t² for t = 0 to 2) +  (t²−4t for t = 2 to 4)

= 8units