helpAn object having mass $m$ is initially at rest on a frictionless horizontal surface. At time

$t=0$; a force is applied horizontally to the object, causing it to move in the positive

$x-$direction. The force, in Newtons, is given by $f(t)=12t^2.$

$($a$)$ Given that velocity is the change in displacement with respect to time and the

acceleration is the change in velocity with respect to time. State a second order

ordinary differential equation and two initial conditions of this problem. $($Hint:

The net force on an object is equal to the mass of the object multiplied by the

acceleration of the object$)$

$($b$)$ Let $m=1kg.$ Using Laplace Transform, find the velocity, $v$ and the displacement,

$x$ of the object at $t=2$ seconds.