Question

The relation between time and distance is $t=\alpha x^2+\beta x$, where $\alpha$ and $\beta$ are constants. The retardation is

• A. $2\alpha v^3$
• B. $2\beta v^3$
• C. $2\alpha \beta v^3$
• D.
  $2{\beta }^2{v}^3$

Answer 1

The correct option is A $2\alpha v^3$

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

$\because a=\frac{dv}{dt}=\frac{dv}{dx}.\frac{dx}{dt}$

$a=v\frac{dv}{dx}=\frac{-v.2\alpha }{(2\alpha x+\beta {)}^2}=-2\alpha .v.v^2=-2\alpha v^3$

$\therefore$ Retardation = $2\alpha v^3$