A particle starts moving with initial velocity of 3 m/s along x-axis from origin. Its acceleration  is varying with position  $\left(x\right)$ in parabolic nature with vertex at the origin as shown in figure. A tangent to the graph is drawn at  $x=\sqrt{3}m$. The tangent makes an angle of  ${60}^0$ with the x-axis. At this position the velocity of particle is $\sqrt{\sqrt{3}+k} m/s$  the value of  $k$ is