Consider the motion of a particle described by $x = a \cos t$, $y = a \sin t$, and $z = t$. The trajectory traced by the particle as a function of time is

Explain average acceleration and instantaneous acceleration.

$A$ particle is moving in the $xy$-plane such that its position coordinates are given by $x = (4t + t^2) \text{ m}$ and $y = (2t + \frac{t^2}{2}) \text{ m}$, where $t$ is in seconds. What is the velocity of the particle?

An ant is moving on a plane horizontal surface. The number of degrees of freedom of the ant will be .........

The $x$ and $y$ coordinates of a particle at any time $t$ are given by $x = 5t - 2t^2$ and $y = 10t$ respectively,where $x$ and $y$ are in meters and $t$ is in seconds. The acceleration of the particle at $t = 2 \, s$ is . . . . . . $m/s^2$.

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