The acceleration of a particle increases linearly with time $\left(t\right)$ as $6t$. If the initial velocity of the particle is zero and the particle starts from the origin, then, the distance travelled by the particle in time $t$ will be

An object may have 

$\left(\mathrm{I}\right)$ varying speed without having varying acceleration.

$\left(\mathrm{II}\right)$ varying velocity without having varying speed.

$\left(\mathrm{III}\right)$ non-zero acceleration without having varying velocity.

$\left(\mathrm{IV}\right)$ non-zero acceleration without having varying speed.

Which of the following options is correct?

The velocity $\left(V\right)$-time $\left(t\right)$ graph for the linear motion of an object is shown in the figure. The displacement and distance after $8 \mathrm{s}$, respectively are

Initially, car $A$ is $10.5 \mathrm{m}$ ahead of car $B$. Both start moving at time $t=0$ in the same direction along a straight line. The velocity-time graph of the two cars is shown in the figure. The time when the car $B$ will catch the car $A$ will be