The displacement of a particle is given by $y = a + bt + ct^2 - dt^4$. The initial velocity and acceleration are respectively

If the decrease in velocity is the same in equal intervals of time,then describe the $x-t$ graph.

$A$ body initially at rest is moving with uniform acceleration $a$. Its velocity after $n$ seconds is $v$. The displacement of the body in the last $2 \ s$ is

$A$ car starts from rest and moves with uniform acceleration. Describe the shapes of the $(i)$ $x-t$, $(ii)$ $v-t$, and $(iii)$ $a-t$ graphs for this motion.

$A$ body is moving with a uniform acceleration covers $40\,m$ in the first $4\,s$ and $120\,m$ in next $4\,s.$ Its initial velocity and acceleration are

$A$ student is at a distance of $16 \ m$ from a bus when the bus begins to move with a constant acceleration of $9 \ m \ s^{-2}$. The minimum velocity with which the student should run towards the bus so as to catch it is $\alpha \sqrt{2} \ m \ s^{-1}$. The value of $\alpha$ is