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Particle moving with velocity \mathrm{v=6 \alpha t^2}, the ratio between displacement to acceleration will be-

Option: 1

\mathrm{t^2 / 6}


Option: 2

\mathrm{t^2 / 3}


Option: 3

\mathrm{t / 6}


Option: 4

\mathrm{t / 3}


Answers (1)

best_answer

      Velocity \mathrm{v=\frac{d s}{d t}=6 \alpha t^2}                  ......(1)

Acceleration \mathrm{a=\frac{d v}{d t}=12 \alpha t-0}       ......(2)

Ratio,  Velocity  \mathrm{v=6 \alpha t^2}

    Displacement \mathrm{(s) =\int v d t}

                             \mathrm{s =\int 6 \alpha t^2 d t \\}

                             \mathrm{s =6 \alpha \int t^2 d t=6 \alpha \cdot \frac{t^3}{3} }

                             \mathrm{s =2 \alpha t^3 }

 

Now,  Ratio between displacement to acceleration -
                               \mathrm{\frac{\text { Displacement }}{\text { Acceleration }} =\frac{2 \alpha t^3}{12 \alpha t} }

                                                                 \mathrm{=\frac{t^2}{6} \quad }   Ans.

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Gaurav

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