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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

Grade:Select Grade

2 Answers

Sumit Majumdar IIT Delhi
askIITians Faculty 137 Points
7 years ago
Dear student,
The displacement is given by the expression:
x^{2}=at^{2}+b
Hence, differentiating with respect to time, we get:
2xdx=2atdt\Rightarrow v=\frac{dx}{dt}=\frac{at}{x}=\frac{at}{\sqrt{at^{2}+b}}
Hence,the derivative of velocity 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{ab}{(at^{2}+b)^{\frac{3}{2}}}
Regards
Sumit
Naman Jain
24 Points
5 years ago
A car starts from rest and accelerates at uniform rate of 6 metres per second square for some time then moves at constant speed for sometime and retards is the same winform rate and the total time for the journey is 24 seconds and average speed for journey is 20 metres per second how long does the car move with constant speed

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