Question #e3d6f

1 Answer
Jan 26, 2018

Answer:

#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.