Question

The velocity of particle moving in straight line depends on its displacement in accordance with curve shown in figure
The acceleration of the particle when its displacement becomes equal to $\frac{3x_0}{4}$ is

• A. $\frac{3v_0^2}{4x_0}$
• B. $\frac{v_0^2}{4x_0}$
• C. $\frac{-3v_0^2}{4x_0}$
• D. $\frac{-v_0^2}{4x_0}$

Answer 1

The correct option is A $\frac{3v_0^2}{4x_0}$

From the graph, $v=\frac{v_0}{x_0}x$

$\Rightarrow \frac{dv}{dt}=\frac{v_0}{x_0}\frac{dx}{dt}$ $\Rightarrow a=\frac{v_0}{x_0}v$

$\Rightarrow a=\frac{v_0^2}{x_0^2}x$

At $x=\frac{3x_0}{4}$ $\Rightarrow a=\frac{v_0^2}{x_0^2}\frac{3x_0}{4}$ $\Rightarrow a=\frac{3v_0^2}{4x_0}$