A particle moved rectilinearly. It's displacement X at time to is given by x^2=at^2+b where a and b are constants. It's acceleration at time to is proportional to

I HAVE NOT TAKEN MATH SO PLS EXPLAIN ACCORDINGLY

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Solution

We are given that the displacement of the point is given by the following relation
X2 = 1 + T2 (1)
we know that the acceleration is the double derivative of the displacement. Hence it will be given by d2X / dT2
from equation (1), we get
X = (1 + T2) 1/2
differentiating with respect to T, we get
dX / dT = 1/2 ( 1 + T2) -1/2 x 2T
= T ( 1 + T2) -1/2
So
d2X / dT2 = 1/ ( 1 + T2)1/2 - T2 / (1+T2) 3/2
But
( 1+ T2)1/2 = X [ from (1)]
Thus
d2X / dT2 = [1/ X ] - [(X2 -1) / X3]
= [X2 -X2 +1] / X3
= 1 / X3

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