The relation between time ‘ t ’ and distance ‘ x ’ is t = α x 2 + β x , where α and β are constants. The relation between acceleration a and velocity v is:

Step-by-step solution

Given: t = α x 2 + β x Differentiating w.r.t time, we get d t d x = 2 α x + β ⇒ 1 v = 2 α x + β Differentiating w.r.t time again, we get ⇒ - 1 v 2 d v d t = 2 α d x d t ⇒ d v d t = - 2 α v 3 as v = d x d t ⇒ a = d v d t = - 2 α v 3