Which direction will this object move in at the end of this process?

Question

1. Consider an object with no net force acting on it moving with a constant velocity $v$. It has a momentum $mv$.

2. Now let a force $F_1$ act on the object. Let the direction of this force be opposite (to the direction of the object's constant velocity)

3. The object now undergoes a change in its momentum over time, accelerating in the direction of the force $F_1$

4. Let another force $F_2$ be introduced that is equal in magnitude to $F_1$ but opposite in direction.

Question: What happens to the object now?

Since under the influenced of balanced forces the object can either be at rest or have a constant velocity. If it does have a constant velocity what will be its direction?

And what is the work done by the two forces?

Answer 1

The object will stop to accelerate since the two forces cancel each other. The final velocity v will be $v=v_0+a*t_0$ where $v_0$ is the initial velocity, a the acceleration provided by $F_1$ and $t_0$ the time until $F_2$ is applied. Note that $v_0$ and $a$ most likely have different direction.

Answer 2

Before the second force is added ,the first force imparts a change of momentum Ft where t is the duration of the force, so the total momentum will be mv + ft. and the total work done by this force during this time will be 1/2mv^2 - 1/2m(v+ft/m)^2 when the second force is added it will continue to move at a velocity v+ft/m with zero acceleration. meaning zero work is now being done by the forces