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A PARTICLE MOVES RECTILINEARLY.ITS DISPLACEMENT ‘x’ AT TIME ‘t’ IS GIVEN BY x(square)=at(square)+b. ITS ACCELERATION AT TIME ‘t’ IS PROPORTIONAL TO? (A) 1/x(cube) (B)1/x-1/x(square) (C)-1/x(square) (D)none of these

 
A PARTICLE MOVES RECTILINEARLY.ITS DISPLACEMENT ‘x’ AT TIME ‘t’ IS GIVEN BY x(square)=at(square)+b. ITS ACCELERATION AT TIME ‘t’ IS PROPORTIONAL TO?
(A) 1/x(cube)
(B)1/x-1/x(square)
(C)-1/x(square)
(D)none of these

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1 Answers

Sumit Majumdar IIT Delhi
askIITians Faculty 137 Points
9 years ago
Dear student,
The displacement is given by:
x^{2}=at^{2}+b
Hence the velocity will be given by:
2xdx=2atdt\Rightarrow v=\frac{dx}{dt}=\frac{at}{x}=\frac{at}{\sqrt{at^{2}+b}}
Thus, the acceleration would be given by:
a=\frac{dv}{dt}=\frac{a\sqrt{at^{2}+b}-\frac{a^{2}t^{2}}{\sqrt{at^{2}+b}}}{at^{2}+b}=\frac{b}{\left ( at^{2}+b \right )^{\frac{3}{2}}}
Regards
Sumit

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