Answer:
[tex]\displaystyle \vec a=-\frac{0.5\vec v_o}{t}[/tex]
[tex]\displaystyle \vec F_{net}=-\frac{0.5\vec v_om}{t}[/tex]
[tex]\vec v_f-\vec v_o=-0.5\vec v_o[/tex]
Explanation:
Dynamics
The dynamics of an object on which a net force is applied are explained by Newton's laws. The net force equals the product of the mass of the object by its acceleration
[tex]\vec F_{net}=m\vec a[/tex]
The formulas for the accelerated motion gives us other relevant magnitudes like the velocity
[tex]\vec v_f=\vec v_o+\vec a\ t[/tex]
Since all the magnitudes are vectors, given an initial state and a final state, their average values only depend on the difference of their states.
We know during the move from A to B, and object decreases its veclocity by half. It means
[tex]\vec v_f=0.5\vec v_o[/tex]
It that happened in a time t, then the average acceleration was
[tex]\displaystyle \vec a=\frac{\vec v_f-\vec v_o}{t}[/tex]
[tex]\displaystyle \vec a=\frac{0.5\vec v_o-\vec v_o}{t}[/tex]
[tex]\displaystyle \vec a=-\frac{0.5\vec v_o}{t}[/tex]
If the object has a mass m, the net force is
[tex]\displaystyle \vec F_{net}=m\vec a=-m\ \frac{0.5\vec v_o}{t}[/tex]
[tex]\displaystyle \vec F_{net}=-\frac{0.5\vec v_om}{t}[/tex]
Finally, the average velocity was
[tex]\vec v_f-\vec v_o=-0.5\vec v_o[/tex]
