2. Questions Bank
  3. JEE Main & Advanced
  4. Mathematics
  5. Differential Equations

JEE Main & Advanced Mathematics Differential Equations Question Bank Application of differnetial equations

  • question_answer
    A particle starts at the origin and moves along the x?axis in such a way that its velocity at the point (x, 0) is given by the formula \[\frac{dx}{dt}={{\cos }^{2}}\pi x.\]  Then the particle never reaches the point on [AMU 2000]

    A)                 \[x=\frac{1}{4}\] 

    B)                 \[x=\frac{3}{4}\]

    C)                 \[x=\frac{1}{2}\] 

    D)                 x = 1

    Correct Answer: C

    Solution :

                       Given \[\frac{dx}{dt}={{\cos }^{2}}\pi x\]. Differentiate w.r.t. t,         \[\frac{{{d}^{2}}x}{d{{t}^{2}}}=-2\pi \sin 2\pi x=-ve\]         \[\because \] \[\frac{{{d}^{2}}x}{d{{t}^{2}}}=0\] Þ \[-2\pi \sin 2\pi x=0\] Þ \[\sin 2\pi x=\sin \pi \]                 Þ \[2\pi x=\pi \] Þ \[x=1/2\].


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