Question

During the move from A to B, the velocity decreases by half. Determine vectors for the average acceleration, average Fnet, and average velocity during the trip?

Answer 1

Answer:

$\displaystyle \vec a=-\frac{0.5\vec v_o}{t}$

$\displaystyle \vec F_{net}=-\frac{0.5\vec v_om}{t}$

$\vec v_f-\vec v_o=-0.5\vec v_o$

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

$\vec F_{net}=m\vec a$

The formulas for the accelerated motion gives us other relevant magnitudes like the velocity

$\vec v_f=\vec v_o+\vec a\ t$

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

$\vec v_f=0.5\vec v_o$

It that happened in a time t, then the average acceleration was

$\displaystyle \vec a=\frac{\vec v_f-\vec v_o}{t}$

$\displaystyle \vec a=\frac{0.5\vec v_o-\vec v_o}{t}$

$\displaystyle \vec a=-\frac{0.5\vec v_o}{t}$

If the object has a mass m, the net force is

$\displaystyle \vec F_{net}=m\vec a=-m\ \frac{0.5\vec v_o}{t}$

$\displaystyle \vec F_{net}=-\frac{0.5\vec v_om}{t}$

Finally, the average velocity was

$\vec v_f-\vec v_o=-0.5\vec v_o$