A particle starts from origin and is moving in $x-y$ plane whose velocity is $v=by\hat{i}+v_0\hat{j}$. The trajectory of particle is

Q. A particle is moving in a plane with velocity given by $y={\nu }_{0}i+\left(\alpha \omega cos\omega t\right)j,$where i , j are units vectors along $x$ and $y$axes respectively .The trajectory of the particle if the particle starts from origin at $t=0$ will be

Q. A particle moves along the plane trajectory $y\left(x\right)$ with velocity $v$ whose modulus is constant. Find the radius of curvature at origin if the trajectory has the form of a parabola $y=a{x}^2$.

Q. A particle of charge $q$ and mass $m$ starts moving from the origin under the action of an electric field $\overrightarrow{E}=E_o\hat{i}$ and $\overrightarrow{B}=B_0\hat{i}$ with a velocity $\overrightarrow{v}=v_0\hat{j}$. The speed of the particle will become $2v_0$ after a time

Q. The velocity vector of a particle moving in the xy plane is given by $\overrightarrow{v}=t\hat{i}+x\hat{j}$. If initially, the particle was at origin then the equation of trajectory of the projectile is?

Q. The velocity of a particle moving in the $x-y$ plane is given by $\frac{dx}{dt}=4\pi \sin \left(3\pi t\right)$ and $\frac{dy}{dt}=3\pi \cos \left(3\pi t\right)$. If the particle starts from origin at $t=0$ then the path of the particle is a/an