2. Sample Papers
  3. NEET

NEET Sample Paper NEET Sample Test Paper-53

  • question_answer
    A particle moves in the plane xy with velocity\[v={{k}_{1}}\,\,i+{{k}_{2}}\,\,x\,\,j\], where i and j are the unit vectors of the x and y axes, and \[{{k}_{1}}\,\,and\,\,{{k}_{\text{2}}}\] are constants. At the initial moment of time the particle was located at the point \[x=y=0\], then the equation of the particle?s trajectory y (x) is-

    A) \[y=\frac{{{k}_{1}}}{2{{k}_{2}}}\,{{x}^{2}}\]         

    B)   \[y=\frac{{{k}_{2}}}{2{{k}_{1}}}\,{{x}^{2}}\]

    C) \[y=\frac{2{{k}_{1}}}{{{k}_{2}}}\,{{x}^{2}}\]                     

    D) \[y=\frac{2{{k}_{2}}}{{{k}_{1}}}\,{{x}^{2}}\]

    Correct Answer: B

    Solution :

    \[v={{k}_{1}}\,i\,\,+\,\,{{k}_{2}}xj\] \[\therefore \,\,\,\text{ }x={{k}_{1}}\,\,t~~~~~~~~\,\,\,\,\,\,\,\,\,.\,..\left( 1 \right)\] \[\And \,\,{{v}_{y}}={{k}_{2}}\,x\,j\] \[\Rightarrow \,\,\frac{dy}{dt}\,\,=\,\,{{k}_{2}}\,{{k}_{1}}\,t\] \[\int{dy\,\,=\,\,\int{{{k}_{2}}\,{{k}_{1}}t\,dt}\,}\] \[\Rightarrow \,\,y\,\,=\,\,{{k}_{1}}{{k}_{2}}\frac{{{t}^{2}}}{2}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,.....(2)\] By (1) & (2) \[y=\frac{{{k}_{2}}}{2{{k}_{1}}}\,{{x}^{2}}\]


You need to login to perform this action.
You will be redirected in 3 sec spinner