Question

A particle is moving along x-axis and velocity '$v$' vs '$x$' graph of particle is as shown in the figure, where $x$ is the displacement of the particle. Find $|\frac{a_1}{a_2}|$, where $a_1$ and $a_2$ are accelerations at points 1 and 2 respectively.

• A. $\frac{\sqrt{3}}{2}$
• B. $\frac{1}{\sqrt{3}}$
• C. $\frac{\sqrt{3}}{4}$
• D. $\frac{1}{2\sqrt{3}}$

Answer 1

The correct option is C $\frac{\sqrt{3}}{4}$

$a=\frac{dv}{dt}=v.\frac{dv}{dx}$

Here, $\frac{dv}{dx}=$ slope of the graph.

$\therefore |\frac{a_1}{a_2}|=|\frac{20}{20}\frac{\tan {37}^{\circ }}{\tan {120}^{\circ }}|=\frac{3/4}{\sqrt{3}}=\frac{3}{4\sqrt{3}}=\frac{\sqrt{3}}{4}$