Question

a particle moves rectilinearly. its displacement 'x' at time 't' is given by x^2=at^2 +b .Its acceleration at time 't'is proportional to..

Answer 1

.................................

Answer 2

Answer:

Acceleration is proportional to 1/(x^3).

Explanation:

Given the displacement as :-

x^2 = at^2 + b.  

Differentiating it with respect to time we get :-

2xdx = 2atdt + 0

Rearranging the terms we have :-  

dx/dt = at/x  (dx/dt is velocity)  .... 1

Now x from the given equation can be written as x = √(at^2 + b)  

Substituting value of x from above to equation number 1 we get :-

dx/dt = at/(√at^2 + b) ...... 2

Now again differentiating equation 2 with respect to time (derivative of velocity is acceleration) we get :-

dv/dt = A( acceleration )  

{ (√at^2 +b)*a - a^2*t^2/(√at^2 +b) }/ (at^2 + b)  

Therefore , A = ab/[(at^2 + b)^3/2] .... 3

Now since x = √(at^2 + b) ....4

From equation 3 and 4 Acceleration is proportional to 1/(x^3).