The $v -t$ graph of a rectilinear motion is shown in adjoining figure. The distance from starting point after $8$ seconds is ..........$metre$

- A
$18 $

- B
$12$

- C
$8$

- D
$6$

Three particles start simultaneously from a point on a horizontal smooth plane. First particle moves with speed $v_1$ towards east, second particle moves towards north with speed $v_2$ and third-one moves towards north-east. The velocity of the third particle, so that the three always lie on a line, is

The acceleration $a$ in $m / s ^2$, of a particle is given by $a=3 t^2+2 t+2$, where $t$ is the time. If the particle starts out with a velocity $v=2 m / s$ at $t=0$, then the velocity at the end of $2\,s$ is $............m/s$

A particle is projected with velocity ${\upsilon _0}$ along $x - axis$. The deceleration on the particle is proportional to the square of the distance from the origin i.e., $a = \alpha {x^2}.$ The distance at which the particle stops is

The position of a particle along $x$-axis at time $t$ is given by $x=2+t-3 t^2$. The displacement and the distance travelled in the interval $t=0$ to $t=1$ are respectively

The path of a particle moving under the influence of a force fixed in magnitude and direction is