At any instant, the velocity and acceleration of a particle moving along a straight line are $v$ and $a$. The speed of the particle is increasing if

Starting from rest, acceleration of a particle is $a = 2(t - 1).$ The velocity of the particle at $t = 5\,s$ is.........$m/sec$

The relation between time ' $t$ ' and distance ' $x$ ' is $t=$ $\alpha x^2+\beta x$, where $\alpha$ and $\beta$ are constants. The relation between acceleration $(a)$ and velocity $(v)$ is:

A particle initially at rest moves along the $x$-axis. Its acceleration varies with time as $a=4\,t$. If it starts from the origin, the distance covered by it in $3\,s$ is $...........\,m$

For the acceleration-time $(a-t)$ graph shown in figure, the change in velocity of particle from $t=0$ to $t=6 \,s$ is ........ $m / s$