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

Average acceleration can be found using Δv/Δt and is negative if the particle is slowing down. Average net force requires the particle's mass and acceleration, which is calculated using Newton's second law. Average velocity is zero if the net displacement is zero.

Step-by-step explanation:

The question deals with finding the average acceleration, average net force (Fnet), and average velocity of a particle during a motion where the velocity decreases by half.

For the average acceleration, one would typically use the formula a_avg = Δv / Δt, where Δv is the change in velocity and Δt is the change in time. Since the velocity is decreasing and acceleration is given as negative when the particle is slowing down, the acceleration vector will also be negative.

To determine average Fnet, one could use Newton's second law, F = ma, once the mass of the object and the average acceleration are known. However, without the mass, we cannot calculate the average net force.

In terms of average velocity, it would be calculated as the total displacement divided by the total time. In a scenario where the net displacement is zero (such as a round trip), the average velocity would also be zero.

Answer 2

`\displaystyle \vec a=-(0.5\vec v_o)/(t)`

`\displaystyle \vec F_(net)=-(0.5\vec v_om)/(t)`

`\vec v_f-\vec v_o=-0.5\vec v_o`

Step-by-step 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=(\vec v_f-\vec v_o)/(t)`

`\displaystyle \vec a=(0.5\vec v_o-\vec v_o)/(t)`

`\displaystyle \vec a=-(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\ (0.5\vec v_o)/(t)`

`\displaystyle \vec F_(net)=-(0.5\vec v_om)/(t)`

Finally, the average velocity was

`\vec v_f-\vec v_o=-0.5\vec v_o`