A50-kg box is being pushed along a horizontal surface. the coefficient of static friction between the box and the ground is 0.65, and the coefficient of kinetic friction is 0.35. what horizontal force must be exerted on the box for it to accelerate at 1.2 m/s2?
a) 60 n
b) 230 n
c) 120 n
d) 170 n
e) 490 n

To solve the exercise it is necessary to apply the concepts related to Newton's Second Law, as well as the definition of Weight and Friction Force.

According to the problem there is a movement in the body and it is necessary to make a sum of forces on it, so that

There are two forces acting on the body, the Force that is pushing and the opposing force that is that of friction, that is

To find the required force then,

By definition we know that the friction force is equal to the multiplication between the friction coefficient and the weight, that is to say

Therefore the horizontal force applied on the block is B) 230N

carla slowed down in the beginning of her trip, stopped, and then sped up

the box does not move because you need to use a force greater than 300 n. you are only using 50 n. it needs to at least be 301 n for the box to move because then it is an unbalanced force and it will move the way that the greater force is pushing it. if you use only 300 n it will be a balanced force and will not move because the force you are exerting on the   box is the same as its force.

hope this !

im sorry if i went too in depth, i am going to include a link to a video on khan academy that will explain this.   hope that you like the video and that it explains more in detail to you.

that is the link.