Physics - Kinematics Question with Solution | TestHub

Given: $t=\alpha x^2+\beta x$ 

Differentiating w.r.t time, we get

$\frac{dt}{dx}=2\alpha x+\beta$

$\Rightarrow \frac{1}{v}=2\alpha x+\beta$

Differentiating w.r.t time again, we get

$\Rightarrow -\frac{1}{v^2}\frac{dv}{dt}=2\alpha \frac{dx}{dt}$

$$\begin{gathered} \Rightarrow \frac{dv}{dt}=-2\alpha v^3\left[\text{as} v=\frac{dx}{dt}\right] \\ \Rightarrow a=\frac{dv}{dt}=-2\alpha v^3 \end{gathered}$$