Question

A particle starts with initial velocity $15\text{m/s}$. 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. $13.65\text{m/s}$
• B. $12.56\text{m/s}$
• C. $17.47\text{m/s}$
• D. $18.64\text{m/s}$

Answer 1

The correct option is C $17.47\text{m/s}$

As we know from the $a-x$ curve that,
$\frac{v^2-u^2}{2}=\text{Area under the curve}$
Given, $u=15\text{m/s}$
$\Rightarrow \frac{v^2-{15}^2}{2}=\frac{1}{2}\times 2\times 10+10\times (5-2)$
$\Rightarrow v^2=225+2\times 40=305\Rightarrow v=\sqrt{305}=17.47\text{m/s}$
Hence, speed of the particle at $x=5\text{m}$ is $17.47\text{m/s}$