The graph of position $x$ versus time $t$ represents the motion of a particle. If $b$ and $c$ are both positive constants, which of the following expressions best describes the acceleration $a$ of the particle?

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

A point moves in $x -y$ plane according to the law $x = 3\, cos\,4t$ and $y = 3\, (1 -sin\,4t)$. The distance travelled by the particle in $2\, sec$ is...........$m$  (where $x$ and $y$ are in $metres$ )

Particles $A$ and $B$ are moving with constant velocities along $x$ and $y$ axis respectively, the graph of separation between them with time is

The co-ordinates of a particle moving in $x-y$ plane are given by :  $\mathrm{x}=2+4 \mathrm{t}, \mathrm{y}=3 \mathrm{t}+8 \mathrm{t}^2 .$ The motion of the particle is :

A football is kicked into the air vertically upwards. What is its

$(a)$ acceleration and

$(b)$ velocity at the highest point ?