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CEE Kerala Engineering CEE Kerala Engineering Solved Paper-2001

  • question_answer
    A particle moves along the\[x-\]axis so that it position is given\[x=2{{t}^{3}}-3{{t}^{2}}\] at a time t seconds. What is the time interval during which particle will be on the negative half of the axis?

    A)  \[0<t<\frac{2}{3}\]        

    B)         \[0<t<1\]

    C)  \[0<t<\frac{3}{2}\]        

    D)         \[\frac{1}{2}<t<1\]

    E)  \[1<t<\frac{3}{2}\]

    Correct Answer: C

    Solution :

    For the particle to be on the negative half of the axis \[x<0\] \[\therefore \]  \[2{{t}^{3}}-3{{t}^{2}}<0\] \[\Rightarrow \]               \[{{t}^{2}}(2t-3)<0\] \[\Rightarrow \]               \[t>0,t<\frac{3}{2}\] (\[\because \]time cannot be negative) \[\therefore \]  \[0<t<\frac{3}{2}\]


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