The displacement of a particle is given by x=(t−2)2 where x is in metres and t is in seconds. The distance 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 to2

=t2−4t for t=2 to 4

= 8 units