Question

A 30 kg student pushes a 20kg box on frictionless surface. If student accelerates at 0.8m/s^2(N),what is acceleration of bix. now why does the box acceerate towards south, if it is being pushed north should it not move north.

Answer 1

Before the push, the momentum of the system was zero
so since there is no EXTERNAL force on the student/box system,
After the push the total momentum of the system is zero.

Therefore
If the student goes North
then
The box goes South

if north is +
.8 (30) + v (20) = 0
v = -.8(30/20)

Answer 2

PS

Perhaps you missed that word "frictionless"

Do not think you are pushing that box along a hockey rink. That requires friction and cleats on your shoes if on ice.
If no cleats, if the box goes one way you go the other :)

Answer 3

The answer would be 1.2 m/s^2.
Since the student is pushing against the box, the amount of force they are using is equivalent to the amount of force the box is pushing back (As explained by Newton's third law of motion). Therefore, you first have to find the amount of force the student is using, and then set that equal to the mass of the box to find its acceleration.
F(of the student)=ma
=30(.8)
=24N
F(student)=f(box)
24N=ma
24=20(a)
acceleration of the box= 24/20= 1.2 m/s^2