$A$ particle moves along a straight line such that its displacement at any time $t$ is given by $s = t^3 - 6t^2 + 3t + 4 \text{ m}$. The velocity when the acceleration is zero is ........ $m s^{-1}$.

$A$ body travels $102.5 \ m$ in the $n^{\text{th}}$ second and $115.0 \ m$ in the $(n+2)^{\text{th}}$ second. The acceleration is: (in $m/s^2$)

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.

Derive the equations of uniformly accelerated motion by the graphical method.

The velocity acquired by a body moving with uniform acceleration is $30 \ m/s$ in $2 \ s$ and $60 \ m/s$ in $4 \ s$. The initial velocity is $............. \ m/s$.

$A$ particle starting from rest and moving with a uniform acceleration along a straight line covers distances $a$ and $b$ in successive intervals of $p$ and $q$ seconds. The acceleration of the particle is