Question

Question #e3d6f

Answer 1

`a=F_"net"/m`

Explanation:

Basically equation of motion is solving Newton's 2nd Law.

Assuming

`F_"net" = ma`
`a = F_"net"/m`
`a = dv/dt = d/dt(dx/dt)= (d^2x)/(d^2t)`

Unless we know the nature of F, we just solve for

`rArr (d^2x)/(d^2t)=a`

Otherwise, to get the proper solution, you need to solve
`(d^2x)/(d^2t) = F_"net"/m`

Perform integration twice and applying proper initial conditions
`Deltax = int inta (t')dt'dt`
`rArr x =x_0+int inta (t')dt'dt`

If start from rest, `v_0=0 and a (t) = constant =a`

`rArr x =x_0+ v_0t + 1/2at^2 = x_0 + 1/2at^2`

Of course, the exact form will depend on the nature of force is being applied too. For instant, if F is caused by a spring pulling on the mass, then solution involves a sinusoidal displacement.