Question #e3d6f

1 Answer
MetaPhysik
Jan 26, 2018

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.

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