Question

A particle starts from rest. The $a-x$ curve is shown in the figure for the motion of particle. The speed of the particle at $x=5\text{m}$ is

• A. $\sqrt{80}\text{m/s}$
• B. $\sqrt{40}\text{m/s}$
• C. $\sqrt{50}\text{m/s}$
• D. $\sqrt{60}\text{m/s}$

Answer 1

The correct option is A $\sqrt{80}\text{m/s}$

As we know from the $a-x$ curve that,
$\frac{v^2-u^2}{2}=\text{Area under the curve}$
Given, $u=0$
$\Rightarrow \frac{v^2}{2}=\frac{1}{2}\times 2\times 10+10\times (5-2)$
$\Rightarrow v^2=2\times 40=80\Rightarrow v=\sqrt{80}\text{m/s}$
Hence, speed of the particle at $x=5\text{m}$ is $\sqrt{80}\text{m/s}$