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2.Motion in Straight Line
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A particle located at $x= 0$ at time $ t= 0 $, starts moving along with the positive $x-$direction with a velocity $v$ that varies as $v$ $=$ $\alpha \sqrt x $. The displacement of the particle varies with time as
A
$t^3$
B
$t^2$
C
$t$
D
${t^{\frac{1}{2}}}$
(AIEEE-2006)
Solution
$v=\frac{d x}{d t}=\alpha \sqrt{x}$
$\therefore \frac{d x}{\sqrt{x}}=\alpha d t$
$\int \frac{d x}{\sqrt{x}}=\alpha \int d t$
$\therefore 2 x^{1 / 2}=\alpha t$
$\therefore x \propto t^{2}$
Standard 11
Physics
Similar Questions
Let us cell a motion, $A$ when velocity is positive and increasing $A^{-1}$ when velocity is negative and increasing. $R$ when velocity is positive and decreasing and $R^{-1}$ when velocity is negative and decreasing. Now, match the following two columns for the given $s=t$ graph.
| Colum $I$ | Colum $II$ |
| $(A)$ $M$ | $(p)$ $A^{-1}$ |
| $(B)$ $N$ | $(q)$ $R^{-1}$ |
| $(C)$ $P$ | $(r)$ $A$ |
| $(D)$ $Q$ | $(s)$ $R$ |
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