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2.Motion in Straight Line
medium
The initial velocity of a particle moving along $x$-axis is $u$ (at $t=0$ and $x=0$ ) and its acceleration $a$ is given by $a=k x$. Which of the following equation is correct between its velocity $(v)$ and position $(x)$ ?
A
$v^2-u^2=2 k x$
B
$v^2=u^2+2 k x^2$
C
$v^2=u^2+k x^2$
D
$v^2+u^2=2 k x$
Solution
(c)
$a=k x \text { and } \frac{v d v}{d x}=a$
$\Rightarrow \int \limits_u^v v d v=\int \limits_0^x a d x=\int \limits_0^x k x d x$
$\left.\Rightarrow \frac{v^2}{2}\right|_u ^v=\left.\frac{k x^2}{2}\right|_0 ^x$
$\Rightarrow v^2-u^2=k x^2 \Rightarrow v^2=u^2+k x^2$
Standard 11
Physics
