The relation between time and distance is t = x ^2+ x, where and … - Vidyadip

MCQ

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

✓
$2 \alpha v^3$
B
$2 \beta v^3$
C
$2 \alpha \beta v^3$
D
$2 \beta^2 v^3$

✓

Answer

Correct option: A.

$2 \alpha v^3$

(A)
$\frac{d t}{d x}=2 \alpha x+\beta \Rightarrow v=\frac{1}{2 \alpha x+\beta}$
$\because \quad a =\frac{ dv }{ dt }=\frac{ dv }{ dx } \cdot \frac{ dx }{ dt }$
$a=v \frac{d v}{d x}=\frac{-v 2 \alpha}{(2 \alpha x+\beta)^2}=-2 \alpha v v^2=-2 \alpha v^3$
Retardation $=2 \alpha v ^3$

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