The acceleration of a particle which moves along the positive $x-$axis varies with its position as shown. If the velocity of the particle is $0.8 m/s$ at $x = 0$ , the velocity of the particle at $x = 1.4$ is(in $m/s$)

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 displacement of a particle from a point having position vector $2 \hat{i}+4 \hat{j}$ to another point having position vector $5 \hat{i}+1 \hat{j}$ is ........ units

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 $metres$ )

An aircraft is flying at a height of $3400\; m$ above the ground. If the angle subtended at a ground observation point by the aircraft positions $10.0\; s$ apart is $30^o$, what is the speed in $m/s$ of the aircraft ?

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