question_answer 33)

                  The displacement of a particle is given by \[x={{(t-2)}^{2}}\] where \[x\] is in metres and t in seconds. The distance covered by the particle in first 4 seconds is                 (a) 4 m                                  (b) 8 m                 (c) 12 m                                (d) 16 m                

Answer:

                  (b) At \[t\,=\,0,\,{{x}_{0}}\,=\,4m.\]                 \[\upsilon =\,2(t-2)\]                 and \[a=2\,m\,{{s}^{-2}}\]                         At     \[t=2,\,\upsilon =0\]                 \[\therefore \] from \[t=2\] to \[t=4s\]                 \[x\,=\frac{1}{2}\,\,a\,{{t}_{2}}\,=\,4\,m\]                 \[\therefore \] Distance covered in first four seconds\[={{x}_{0}}\,+\,x\,=8\,m\]