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JEE Main & Advanced Physics Motion in a Straight Line / सरल रेखा में गति Question Bank Non-uniform Motion

  • question_answer
    The acceleration \['a'\] in \[m/{{s}^{2}}\] of a particle is given by \[a=3{{t}^{2}}+2t+2\] where \[t\] is the time. If the particle starts out with a velocity  \[u=2\,m/s\] at \[t=0\], then the velocity at the end of  2 second is              [MNR 1994; SCRA 1994]

    A)             12 m/s

    B)             18 m/s

    C)             27 m/s

    D)                         36 m/s

    Correct Answer: B

    Solution :

                    \[v=u+\int_{{}}^{{}}{adt=u+\int_{{}}^{{}}{(3{{t}^{2}}+2t+2)dt}}\]             \[=u+\frac{3{{t}^{3}}}{3}+\frac{2{{t}^{2}}}{2}+2t=u+{{t}^{3}}+{{t}^{2}}+2t\]             \[=2+8+4+4=18\ m/s\]                    (As t = 2 sec)


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