The $x$ and $y$ coordinates of a particle at any time $t$ are given by $x = 7t + 4t^2$ and $y = 5t$,where $x$ and $y$ are in $m$ and $t$ is in $s$. The acceleration of the particle at $t = 5 \ s$ is ......... $m/s^2$.

Explain average velocity,instantaneous velocity,and components of velocity for motion in a plane.

Which two motions are considered to be combined for motion in a plane?

The coordinates of a moving particle at any time $t$ are given by $x = \alpha t^3$ and $y = \beta t^3$. The speed of the particle at time $t$ is given by

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 $t = 1.0 \ s$.

$A$ hall has the dimensions $10\,m \times 12\,m \times 14\,m$. $A$ fly starting at one corner ends up at a diametrically opposite corner. What is the magnitude of its displacement in meters?