$A$ point moves in the $x-y$ plane according to $x = kt$ and $y = kt(1 - \alpha t)$,where $k$ and $\alpha$ are positive constants. The equation of the trajectory is:

The coordinates of a particle moving in the $XY$-plane vary with time as $x = 4t^2$ and $y = 2t$. The locus of the particle is a:

The position of a particle is given by $r = 3.0 t \hat{i} + 2.0 t^{2} \hat{j} + 5.0 \hat{k}$,where $t$ is in seconds and the coefficients have the proper units for $r$ to be in metres. $(a)$ Find $v(t)$ and $a(t)$ of the particle. $(b)$ Find the magnitude and direction of $v(t)$ at $t = 1.0 \ s$.

The position of a particle is given by $\vec{r} = 3.0 t \hat{i} - 2.0 t^{2} \hat{j} + 4.0 \hat{k} \; m$,where $t$ is in seconds and the coefficients have the proper units for $\vec{r}$ to be in metres.
$(a)$ Find the velocity $\vec{v}$ and acceleration $\vec{a}$ of the particle.
$(b)$ What is the magnitude and direction of velocity of the particle at $t = 2.0 \; s$?

Give examples of one-dimensional,two-dimensional,and three-dimensional motion.

An aeroplane flies $400 \,m$ north and $300 \,m$ south and then flies $1200 \,m$ upwards. The net displacement is...........$m$.