If x=a t^2 and y=2 a t , then d^2 y d x^2 at t= 1 2 is

Step-by-step solution

We have, x=a t^2 d x d t =2 a t d t d x = 1 2 a t and y=2 a t d y d t =2 a d y d x = d y / d t d x / d t = 2 a 2 a t = 1 t Differentiating w.r.t x , we get aligned & Now, d^2 y d x^2 = -1 t^2 d t d x = -1 t^2 1 (2 a t) [ d t d x = 1 2 a t ] & = -1 2 a t^3 aligned At t= 1 2 ( d^2 y d x^2 )_ t= 1 2 = -1 2 a 1 8 = -4 a