The velocity of a particle is $v = v_0 + gt + ft^2$. If its position is $x = 0$ at $t = 0$,then its displacement after unit time $(t = 1)$ is

The motion of a particle is described by the equation $v = at$. The distance travelled by the particle in the first $4 \ s$ is: (in $a$)

Object $A$ starts from rest with a constant acceleration $a$. Object $B$ starts from the same position and moves in the same direction as $A$ with a constant velocity $v$. If both meet after time $t$,then $t =$

$A$ three-wheeler starts from rest,accelerates uniformly with $1\; m/s^{2}$ on a straight road for $10\; s$,and then moves with uniform velocity. Plot the distance covered by the vehicle during the $n^{\text{th}}$ second $(n = 1, 2, 3, \ldots)$ versus $n$. What do you expect this plot to be during accelerated motion: a straight line or a parabola?

The velocity $u$ and displacement $r$ of a body are related as $u^2 = kr$,where $k$ is a constant. What will be the velocity after $1 \, s$? (Given that the displacement is zero at $t = 0$)

Give examples of a one-dimensional motion where:
$(a)$ The particle moving along positive $x$-direction comes to rest periodically and moves forward.
$(b)$ The particle moving along positive $x$-direction comes to rest periodically and moves backward.