A particle has an initial velocity of ($3\hat i + 4\hat j)\;ms^{-1}$ and an acceleration of $(0.4\hat i + 0.3\hat j)\;ms^{-1}$ Its speed after $10\;s$ is:

A particle moves in a plane along an elliptic path given by $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$. At point $(0, b)$, the $x$-component of velocity is $u$. The $y$-component of acceleration at this point is

A particle has initial velocity of $\left( {\widehat i + \widehat j} \right)\, m/s$ and an acceleration of $\left( {\widehat i + \widehat j} \right)\, m/s^2$. Its speed after $10s$ will be :-

A vector has magnitude and direction. Does it have a location in space ? Can it vary with time ? Will two equal vectors $a$ and $b$ at different locations in space necessarily have identical physical effects ? Give examples in support of your answer.

The position vector of a particle is given as $\vec r\, = \,({t^2}\, - \,8t\, + \,12)\,\hat i\,\, + \,\,{t^2}\hat j$ The time after which velocity vector and acceleration vector becomes perpendicular to each other is equal to........$sec$

Motion of a particle in $x - y$ plane is described by a set of following equations $x=4 \sin \left(\frac{\pi}{2}-\omega t\right) m$ and $y=4 \sin (\omega t) m$. The path of particle will be