• # question_answer A particle starts from rest. The variation of its acceleration (a) with time (f) is as shown in figure. Then choose the correct statement. A)  Velocity at $t=8s$is$27\,m/s$B)  Velocity is maximum at $t=8s$C)  Velocity at t = 12 is 20 m/sD)  All of the above.

Let the velocity at the end of 4 s be${{u}_{1}}.$ Using $v=u+$ at from t = 0 to t = 4 s yields ${{u}_{1}}=5\times 4=20\,m/s$ Let the velocity at the end of 8 s be ${{u}_{2}}.$Invoking $v=u+at$at from             $t=4$to $t=8\,s$yields. ${{u}_{2}}={{u}_{1}}+2\times 4\Rightarrow {{u}_{2}}=20+2\times 4=28\,m/s.$ The acceleration remains positive from t = 0 to $t=8\,s.$Hence the magnitude of the velocity is maximum at$t=8\,s.$ Let the velocity of the body be ${{u}_{3}}$ at the end of 12 s. Invoking $v=u+$at from $t=8\,s$to $t=12\,s$yields             ${{u}_{3}}=28-2\times 4=20\,m/s.$ Hence, the correction option is (d).