Velocity of a particle moving in a curvilinear path in a horizontal $X$ $Y$ plane varies with time as $\vec v = (2t\hat i + t^2 \hat j) \ \ m/s.$ Here, $t$ is in second. At $t = 1\ s$
acceleration of particle is $8\ m/s^2$
tangential acceleration of particle is $\frac{4}{{\sqrt 5 }} \ m/s^2$
radial acceleration of particle is $\frac{6}{{\sqrt 5 }} \ m/s^2$
radius of curvature to the path is $\frac{5\sqrt 5}{{2 }} \ m$
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........$sec$
The position vector of a particle $\vec R$ as a function of time is given by $\overrightarrow {\;R} = 4\sin \left( {2\pi t} \right)\hat i + 4\cos \left( {2\pi t} \right)\hat j$ where $R$ is in meters, $t$ is in seconds and $\hat i$ and $\hat j$ denote unit vectors along $x-$ and $y-$directions, respectively. Which one of the following statements is wrong for the motion of particle?
and direction of the vectors $\hat{ i }+\hat{ j }$, and $\hat{ i }-\hat{ j }$ ? What are the components of a vector $A =2 \hat{ i }+3 \hat{ j }$ along the directions of $\hat{ i }+\hat{ j }$ and $\hat{ i }-\hat{ j } ?$
A particle starts moving rectilinearly at time $t = 0$ such that its velocity $'v'$ changes with time $'t'$ according to the equation $v = t^2 - t$ where $t$ is in seconds and $v$ is in $m/s.$ The time interval for which the particle retards is