Question

If acceleration is constant and initial velocity of the body is $0$, then choose the correct statement. Symbols have their usual meaning.

• A. $v\propto \sqrt{t}$
• B. $v\propto \sqrt{x}$
• C. $v\propto t$
• D. $v\propto x^2$

Answer 1

Answer: (B), (C)

The correct options are
B $v\propto \sqrt{x}$
C $v\propto t$

$\left(B\right),\left(C\right)$

$a=k$ (constant)

$a=\frac{dV}{dt}$

$\therefore V=\int adt$

$V=kt+C$

at $t=0$, $V=0$

$\therefore V=kt+C\Rightarrow O=O+C\Rightarrow C=0$

$\therefore$ $V=kt$ $\Rightarrow V\alpha t\to \left(1\right)$

$x=\int Vdt$

$=\frac{{kt}^2}{2}+C_1$

assume that $x=0$ at $t=0$

$\Rightarrow C_1=0$

$\therefore x=\frac{{kt}^2}{2}\Rightarrow x\alpha t^2$

$\Rightarrow t\alpha \sqrt{x}\to \left(2\right)$

$\left(2\right)$ in $\left(1\right)$ $\Rightarrow V\alpha \sqrt{x}$