A particle starts from the origin at $t=0$ $s$ with a velocity of $10.0 \hat{ j } \;m / s$ and moves in the $x-y$ plane with a constant acceleration of $(8.0 \hat{ i }+2.0 \hat{ j }) \;m \,s ^{-2} .$
$(a)$ At what time is the $x$ - coordinate of the particle $16\; m ?$ What is the $y$ -coordinate of the particle at that time?
$(b)$ What is the speed of the particle at the time?
Consider a point $P$ on the circumference of a disc rolling along a horizontal surface. If $R$ is the radius of the disc, the distance through which $P$ moves in one full rotation of the disc is
A particle moves such that its position vector $\overrightarrow{\mathrm{r}}(\mathrm{t})=\cos \omega \mathrm{t} \hat{\mathrm{i}}+\sin \omega \mathrm{t} \hat{\mathrm{j}}$ where $\omega$ is a constant and $t$ is time. Then which of the following statements is true for the velocity $\overrightarrow{\mathrm{v}}(\mathrm{t})$ and acceleration $\overrightarrow{\mathrm{a}}(\mathrm{t})$ of the particle