The correct option is B 1x3
Given, x2=1+t2
Differentiating the above equation we get
2xdx=2tdt⇒ xdxdt=t.........(i)
Now, taking differentiation of above equation for acceleration we get,
xd2xdt2+(dxdt)2=1
Or, xd2xdt2=1−(tx)2
⇒ d2xdt2=x2−t2x3=1x3 (∵ x2=1+t2⇒ x2−t2=1)
Hence, the acceleration is a=d2xdt2=1x3 m/s2