2. Sample Papers
  3. NEET

NEET Sample Paper NEET Sample Test Paper-47

  • question_answer
    A particle moving along x-axis has acceleration f, at time t, given by\[\operatorname{f} = {{f}_{o}}\left[ 1-\frac{t}{T} \right]\], where \[{{\operatorname{f}}_{o}}\]and T are constants. The particle at t = 0 has zero velocity. In the time interval between t = 0 and the instant when f = 0, the particle's velocity \[\left( {{v}_{x}} \right)\] is:

    A) \[{{\operatorname{f}}_{o}}T\]              

    B) \[{{\operatorname{f}}_{o}}{{T}^{2}}\]  

    C) \[{{\operatorname{f}}_{o}}^{2}{{T}^{2}}\]                          

    D) \[\frac{{{\operatorname{f}}_{o}}T}{2}\]

    Correct Answer: D

    Solution :

    \[\operatorname{f}={{f}_{o}}-\frac{{{f}_{o}}t}{T}\] \[\operatorname{f}=\frac{dv}{dt}={{f}_{o}}-\frac{{{f}_{o}}t}{T}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\left[ \operatorname{a}=f=\frac{dv}{dt} \right]\] \[dv={{f}_{o}}\operatorname{dt}-\frac{{{f}_{o}}t}{T}\] Integrating both sides \[\operatorname{v}={{f}_{o}}t-\frac{{{f}_{o}}{{t}^{2}}}{T\times 2};t=0,\,\,v=0\] \[{{f}_{o}}-\frac{{{f}_{o}}t}{T}=0,t=T\] \[\operatorname{v} at t = T\] \[\operatorname{v}={{f}_{o}}T-\frac{{{f}_{o}}{{T}^{2}}}{2T}\] \[\operatorname{v}=\frac{{{f}_{o}}\operatorname{T}}{2}\]


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