MCQ
The velocity $v$ of a particle moving along $x$-axis varies with its position $(x)$ as $v=\alpha \sqrt{x}$; where $\alpha$ is a constant. Which of the following graph represents the variation of its acceleration (a) with time $(t)$ ?
- A
- B
- ✓
- D
✓
Answer
Correct option: C.
c
(c)
(c)
$v=\alpha \sqrt{x}$
Squaring both sides $v^2=\alpha^2 x$
Comparing above equation with $3^{\text {rd }}$ equation of kinematics.
$v^2=u^2+2 a x$
$\alpha^2 x =2 a x$
$\Rightarrow a=\frac{\alpha^2}{2}$
$\,\downarrow$
$\text { Constant } \rightarrow \text { not a function of time }$
so,
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