The figure shows a velocity-time graph of a particle moving along a straight line  The correct acceleration-time graph of the particle is shown as

$Assertion$ : A tennis ball bounces higher on hills than in plains.
$Reason$ : Acceleration due to gravity on the hill is greater than that on the surface of earth

The position of a particle is given by

$r =3.0 t \hat{ i }-2.0 t^{2} \hat{ j }+4.0 \hat{ k } \;m$

where $t$ is in seconds and the coefficients have the proper units for $r$ to be in metres.

$(a)$ Find the $v$ and a of the particle?

$(b)$ What is the magnitude and direction of velocity of the particle at $t=2.0 \;s ?$

Acceleration versus velocity graph of a particle moving in a straight line starting from rest is as shown in figure. The corresponding velocity-time graph would be

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 $metres$ )

The figure shows a velocity-time graph of a particle moving along a straight line  The total distance travelled by the particle is  ........ $m$